Finite automata and consolidate bash/POSIX.

2024-12-23 20:32:13 -07:00 · 2024-12-23 20:32:13 -07:00 · 737ed9e300
parent e82c40f662
commit 737ed9e300
25 changed files with 1260 additions and 255 deletions
--- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
+++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
@ -237,7 +237,10 @@
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--- a/notes/_journal/2024-12-21.md
+++ b/notes/_journal/2024-12-21.md
@ -1,9 +0,0 @@
 ---
 title: "2024-12-21"
 ---
 - [x] Anki Flashcards
 - [x] KoL
 - [x] OGS
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
--- a/notes/_journal/2024-12-23.md
+++ b/notes/_journal/2024-12-23.md
@ -0,0 +1,11 @@
 ---
 title: "2024-12-23"
 ---
 - [x] Anki Flashcards
 - [x] KoL
 - [ ] OGS
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 * Added [[automaton|finite automata]] definition and related introductory notes.
--- a/notes/_journal/2024-12/2024-12-21.md
+++ b/notes/_journal/2024-12/2024-12-21.md
@ -0,0 +1,12 @@
 ---
 title: "2024-12-21"
 ---
 - [x] Anki Flashcards
 - [x] KoL
 - [x] OGS
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 * Notes on properties of [[integrals#Step Functions|step function integrals]].
 * Additional notes on [[cardinality|cardinal numbers]].
--- a/notes/_journal/2024-12/2024-12-22.md
+++ b/notes/_journal/2024-12/2024-12-22.md
@ -0,0 +1,11 @@
 ---
 title: "2024-12-22"
 ---
 - [x] Anki Flashcards
 - [x] KoL
 - [x] OGS
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 * Notes on [[language]] (e.g. strings, alphabets, etc.).
--- a/notes/algebra/set.md
+++ b/notes/algebra/set.md
@ -366,7 +366,7 @@ For any sets $A$, $B$, and $C$, $$\begin{align*} A \cap (B \cup C) & = (A \cap B
 %%ANKI
 Basic
 The distributive laws of the algebra of sets apply to what operators?
-Back: $\cup$ and $\cap$
+Back: $\cup$ and $\cap$.
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1716803270441-->
 END%%
--- a/notes/bash/index.md
+++ b/notes/bash/index.md
@ -1,43 +0,0 @@
 ---
 title: Bash
 TARGET DECK: Obsidian::STEM
 FILE TAGS: bash
 tags:
  - bash
 ---
 %%ANKI
 Basic
 How do you escape a `'` within a single-quote string?
 Back: This is impossible.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752230-->
 END%%
 %%ANKI
 Basic
 What does the null string refer to?
 Back: The empty string, i.e. `""`.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752237-->
 END%%
 %%ANKI
 Basic
 When does Bash remove null strings from a command?
 Back: When they occur as part of a non-null command-line argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752241-->
 END%%
 %%ANKI
 Basic
 Why does the following not work correctly?
 ```bash
 $ # -F specifies the field separator
 $ awk -F"" 'program' files
 ```
 Back: Bash removes the null string before executing the command.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816764555-->
 END%%
--- a/notes/bash/prompts.md
+++ b/notes/bash/prompts.md
@ -1,61 +0,0 @@
 ---
 title: Prompts
 TARGET DECK: Obsidian::STEM
 FILE TAGS: bash
 tags:
  - bash
 ---
 ## Overview
 According to Robbins a POSIX-compliant shell (like Bash) generally has the primary and secondary prompts denoted with `$` and `>` respectively. Adjust these values using environment variables `$PS1` and `PS2` respectively.
 %%ANKI
 Basic
 What symbol is usually used to denote the primary prompt?
 Back: `$$`
 Reference:  Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706882670149-->
 END%%
 %%ANKI
 Basic
 What environment variable controls Bash's primary prompt?
 Back: `$$PS1`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706973587222-->
 END%%
 %%ANKI
 Basic
 What symbol is usually used to denote the secondary prompt?
 Back: `>`
 Reference:  Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706882670158-->
 END%%
 %%ANKI
 Basic
 What environment variable controls Bash's secondary prompt?
 Back: `$$PS2`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706973587232-->
 END%%
 Paths supplied to commands are typically "sanitized" by prefixing the path name with `./`. This is mentioned in a few different places:
 * `find -execdir` performs this prefixing automatically on all found files.
 * `awk` ambiguously interprets a file named e.g. `count=1` as variable assignment. Should write `$ awk -f program.awk ./count=1`.
 %%ANKI
 Basic
 What methodology is commonly used to "sanitize" paths supplied as command-line arguments?
 Back: Prefixing the paths with `./`.
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706885111460-->
 END%%
 ## Bibliography
 * Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 * Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
--- a/notes/bash/robustness.md
+++ b/notes/bash/robustness.md
@ -1,69 +0,0 @@
 ---
 title: Measuring Command Robustness
 TARGET DECK: Obsidian::STEM
 FILE TAGS: bash
 tags:
  - bash
  - shell
 ---
 ## Overview
 An interesting point Robbins discusses in his introduction to [[posix/awk/index|gawk]] is this idea of command robustness. He states that:
 > A self-contained shell script is more reliable because there are no other files to misplace.
 %%ANKI
 Basic
 What is a self-contained shell script?
 Back: A shell script that does not rely on the presence of other files.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911473-->
 END%%
 %%ANKI
 Basic
 What makes a self-contained shell script more reliable?
 Back: There are no other files to misplace.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911475-->
 END%%
 He argues that the first command below is more robust than the second since the command is more loosely coupled to its environment:
 ```bash
 $ awk 'program' input-file1 input-file2 ...
 $ awk -f program-file input-file1 input-file2 ...
 ```
 It's interesting to think what else can be used as a measure of a command's robustness:
 * Required environment variables or environment variables formatted in a certain way
 	* `$PATH` needs to point to a specific location
 * Whether the invoked program is present by default in a distribution or must be installed
 * The ability to run with or without an associated TTY
 * The ability to run with or without associated standard streams
 	* `stdout`, `stderr`, `stdin`
 * How backwards compatible the invoked program is
 	* Version mismatch may silently cause the same invocation to fail
 * Expected permissions
 	* EUID, read permissions on an input file, etc.
 * Determinism of the program itself
 	* Does output rely entirely on input or can it make nondeterministic choices
 * The amount of resources dedicated to the program
 	* Failure may occur if not enough memory is provided to the command
 * Whether a program acts idempotently
 	* What happens if I run the command twice in a row?
 * Whether a program acts atomically
 	* Is it possible intermediate files are left that affect subsequent runs?
 * The presence of timeouts
 	* Perhaps a program waits a specified amount of time before input is available. The command's success is now externally determined.
 * Locale-aware functionality
 	* Consider for instance [[posix/awk/index|gawk]]'s `\u` [[escape-sequences|sequence]] which targets characters in the current locale's character set as opposed to specifically Unicode.
 	* POSIX standard [[posix/regexp#Character Classes|character classes]] serve as another example.
 The above scenarios are what makes something like [[nix/index|nix]] so compelling.
 ## Bibliography
 * Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
--- a/notes/bash/shebang.md
+++ b/notes/bash/shebang.md
@ -1,58 +0,0 @@
 ---
 title: Shebang
 TARGET DECK: Obsidian::STEM
 FILE TAGS: bash
 tags:
  - bash
 ---
 ## Overview
 The shebang (also writting shabang or sha-bang) is a magic character at the start of a script indicating what command should be run when invoking the script directly. It always begins with ASCII characters `#!`.
 %%ANKI
 Basic
 What ASCII characters do shebangs start with?
 Back: `#!`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706726911458-->
 END%%
 %%ANKI
 Basic
 What class of programs can be specified in a shebang?
 Back: Interpreters
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911461-->
 END%%
 %%ANKI
 Basic
 The OS will parse a shebang into what three parts?
 Back: `#!`, the interpreter, and the rest of the line as a single argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911464-->
 END%%
 %%ANKI
 Basic
 What gotcha does Robbins highlight with shebang parsing?
 Back: The remainder of the line following the interpreter is passed as a *single* argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911467-->
 END%%
 Some systems limit the length of interpreters to just 32 characters. A simple workaround when encountering this limitation is to introduce a symbolic link.
 %%ANKI
 Basic
 What workaround is used when shebang interpreter names are too long?
 Back: Introduce a symbolic link.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911470-->
 END%%
 ## Bibliography
 * Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 * Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
--- a/notes/calculus/integrals.md
+++ b/notes/calculus/integrals.md
@ -1,18 +1,26 @@
 ---
 title: Integrals
 TARGET DECK: Obsidian::STEM
-FILE TAGS: calculus::integrals
+FILE TAGS: calculus::integral
 tags:
  - calculus
  - integral
 ---
 ## Overview
 The integral is usually defined first in terms of step functions and then general ordinate sets. It is closely tied to [[area]]. In particular, the integral of some nonnegative function on a closed interval is defined so that its area is equal to the area of the ordinate set in question.
 ## Step Functions
 Let $s$ be a step function defined on [[intervals|interval]] $[a, b]$, and let $P = \{x_0, x_1, \ldots, x_n\}$ be a [[intervals#Partitions|partition]] of $[a, b]$ such that $s$ is constant on the open subintervals of $P$. Denote by $s_k$ the constant value that $s$ takes in the $k$th open subinterval, so that $$s(x) = s_k \quad\text{if}\quad x_{k-1} < x < x_k, \quad k = 1, 2, \ldots, n.$$
 The **integral of $s$ from $a$ to $b$**, denoted by the symbol $\int_a^b s(x)\,dx$, is defined by the following formula: $$\int_a^b s(x) \,dx = \sum_{k=1}^n s_k \cdot (x_k - x_{k - 1})$$
 Furthermore, $$\int_a^b s(x) \,dx = -\int_b^a s(x) \,dx$$
 and $$\int_a^a s(x)\,dx = 0.$$
 %%ANKI
 Basic
 Apostol first introduces the integral for the ordinate sets of what kind of function?
@ -132,6 +140,183 @@ Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Int
 <!--ID: 1733520215132-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. How is $\int_b^a s(x) \,dx$ defined?
 Back: As $-\int_a^b s(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555507-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. How is $\int_a^b s(x) \,dx$ defined?
 Back: Given partition $P = \{x_0, x_1, \ldots, x_n\}$ with constant value $s_k$ on the $k$th open subinterval, $$\int_a^b s(x) \,dx = \sum_{k=1}^n s_k \cdot (x_k - x_{k - 1})$$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555512-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What does $\int_a^b s(x) \,dx$ evaluate to after swapping limits of integration?
 Back: As $-\int_b^a s(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555515-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What does $\int_a^a s(x) \,dx$ evaluate to?
 Back: $0$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555518-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What name is given to $a$ in $\int_a^b s(x) \,dx$?
 Back: The lower limit of integration.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555521-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What name is given to $b$ in $\int_a^b s(x) \,dx$?
 Back: The upper limit of integration.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555523-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What name is given to $a$ and $b$ in $\int_a^b s(x) \,dx$?
 Back: The limits of integration.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555526-->
 END%%
 ### Additivity
 Let $s$ and $t$ be step functions defined on $[a, b]$. Then $$\int_a^b s(x) + t(x) \,dx = \int_a^b s(x) \,dx + \int_a^b t(x) \,dx$$
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$. What does the additive property state?
 Back: $\int_a^b s(x) + t(x) \,dx = \int_a^b s(x) \,dx + \int_a^b t(x) \,dx$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463659-->
 END%%
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$. What is the following identity called? $$\int_a^b s(x) + t(x) \,dx = \int_a^b s(x) \,dx + \int_a^b t(x) \,dx$$
 Back: The additive property.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463668-->
 END%%
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$. How is the following more compactly written? $$\int_a^b s(x) \,dx + \int_a^b t(x) \,dx$$
 Back: $\int_a^b s(x) + t(x) \,dx$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463673-->
 END%%
 ### Homogeneousness
 Let $s$ be a step function defined on $[a, b]$. Let $c \in \mathbb{R}$. Then $$\int_a^b c \cdot s(x) \,dx = c\int_a^b s(x) \,dx$$
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What does the homogeneous property state?
 Back: For all $c \in \mathbb{R}$, $\int_a^b c \cdot s(x) \,dx = c \int_a^b s(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463679-->
 END%%
 %%ANKI
 Basic
 Let $s$ be a step function defined over $[a, b]$ and $c \in \mathbb{R}$. What is the following identity called? $$\int_a^b c \cdot s(x) \,dx = c\int_a^b s(x) \,dx$$
 Back: The homogeneous property.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463685-->
 END%%
 ### Linearity
 Let $s$ and $t$ be step functions defined on $[a, b]$. Let $c_1, c_2 \in \mathbb{R}$. Then $$\int_a^b [c_1s(x) + c_2t(x)] \,dx = c_1 \int_a^b s(x) \,dx + c_2 \int_a^b t(x) \,dx$$
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$ and $c_1, c_2 \in \mathbb{R}$. What does the linearity property state?
 Back: $\int_a^b [c_1 s(x) + c_2 t(x)] \,dx = c_1 \int_a^b s(x) \,dx + c_2 \int_a^b t(x) \,dx$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463699-->
 END%%
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$ and $c_1, c_2 \in \mathbb{R}$. What is the following identity called? $$\int_a^b [c_1s(x) + c_2t(x)] \,dx = c_1 \int_a^b s(x) \,dx + c_2 \int_a^b t(x) \,dx$$
 Back: The linearity property.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463704-->
 END%%
 %%ANKI
 Basic
 The linearity property is immediately derived from what other two properties?
 Back: The additive and homogeneous properties.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463710-->
 END%%
 %%ANKI
 Cloze
 The {linearity} property is a combination of the {additive} and {homogenous} properties.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463693-->
 END%%
 ### Comparison Theorem
 Let $s$ and $t$ be step functions defined on $[a, b]$. Suppose $s(x) < t(x)$ for all $x \in [a, b]$. Then $$\int_a^b s(x) \,dx < \int_a^b t(x) \,dx$$
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$. What does the comparison theorem state?
 Back: If $s(x) < t(x)$ for all $x \in [a, b]$, $\int_a^b s(x) \,dx < \int_a^b t(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734815755275-->
 END%%
 %%ANKI
 Basic
 Let $s$ and $t$ be step functions over $[a, b]$ such that $s(x) < t(x)$ for all $x \in [a, b]$. What is the following called? $$\int_a^b s(x) \,dx < \int_a^b t(x) \,dx$$
 Back: The comparison theorem.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734815755282-->
 END%%
 %%ANKI
 Basic
 The comparison theorem of step function integrals corresponds to what property of area?
 Back: The monotone property of area.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734815755285-->
 END%%
 %%ANKI
 Basic
 The monotone property of area corresponds to what theorem of step function integrals?
 Back: The comparison theorem.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734815755288-->
 END%%
 ## Bibliography
 * Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
--- a/notes/calculus/intervals.md
+++ b/notes/calculus/intervals.md
@ -1,7 +1,7 @@
 ---
 title: Intervals
 TARGET DECK: Obsidian::STEM
-FILE TAGS: calculus::intervals
+FILE TAGS: calculus::interval
 tags:
  - calculus
 ---
--- a/notes/computability/automaton.md
+++ b/notes/computability/automaton.md
@ -0,0 +1,501 @@
 ---
 title: Automaton
 TARGET DECK: Obsidian::STEM
 FILE TAGS: computability::automaton
 tags:
  - automaton
  - computability
 ---
 ## Finite Automata
 A **finite automaton** is a $5$-tuple $\langle Q, \Sigma, \delta, q_0, F \rangle$, where
 1. $Q$ is a finite set called the **states**;
 2. $\Sigma$ is a finite set called the alphabet;
 3. $\delta \colon Q \times \Sigma \rightarrow Q$ is the **transition function**;
 4. $q_0 \in Q$ is the **start state**; and
 5. $F \subseteq Q$ is the set of **final states**.
 These automaton are typically denoted using a **state diagram** like below. The start state is indicated by an arrow pointing at it from nowhere. An accept state is denoted with a double circle.
 ![[state-diagram.png]]
 A [[language]] is called a **regular language** if a finite automaton recognizes it.
 %%ANKI
 Basic
 A finite automaton comprises of how many components?
 Back: Five.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643206-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What kind of mathematical entity is $Q$?
 Back: A finite set of states.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643211-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What name is given to $Q$?
 Back: $M$'s states.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643215-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What is $\Sigma$?
 Back: An alphabet.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643218-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What kind of mathematical entity is $\delta$?
 Back: A function.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643221-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What name is given to $\delta$?
 Back: $M$'s transition function.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643224-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What is $\delta$'s domain?
 Back: $Q \times \Sigma$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643227-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What is $\delta$'s codomain?
 Back: $Q$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643230-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What kind of mathematical entity is $q_0$?
 Back: An urelement.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643233-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What name is given to $q_0$?
 Back: $M$'s start state.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643238-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What name is given to $F$?
 Back: $M$'s final states.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643242-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What kind of mathematical entity is $F$?
 Back: A finite set.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643247-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. How does $F$ relate to $Q$?
 Back: $F \subseteq Q$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643252-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. How does $q_0$ relate to $Q$?
 Back: $q_0 \subseteq Q$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643257-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. How does $q_0$ relate to $F$?
 Back: N/A.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643263-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How many start states does $M$ have?
 Back: One.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643267-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How many accept states does $M$ have?
 Back: Zero or more.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643272-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How is $M$'s start state denoted in a state diagram?
 Back: With an arrow pointing to it from nowhere.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643277-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How is $M$'s final states denoted in a state diagram?
 Back: With double circles.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643282-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How is $M$'s transition function denoted in a state diagram?
 Back: As edges to and from states.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643286-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M$. How is $M$'s alphabet denoted in a state diagram?
 Back: With symbols labeling each edge.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643291-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $Q$ evaluate to?
 ![[state-diagram.png]]
 Back: $Q = \{q_1, q_2, q_3\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643296-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $\Sigma$ evaluate to?
 ![[state-diagram.png]]
 Back: $\Sigma = \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643301-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $q_0$ evaluate to?
 ![[state-diagram.png]]
 Back: $q_0 = q_1$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643305-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $\mathop{\text{dom}}\delta$ evaluate to?
 ![[state-diagram.png]]
 Back: $\{q_1, q_2, q_3\} \times \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643309-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $\mathop{\text{ran}}\delta$ evaluate to?
 ![[state-diagram.png]]
 Back: $\{q_1, q_2, q_3\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643313-->
 END%%
 %%ANKI
 Basic
 Consider diagram of finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$. What does $F$ evaluate to?
 ![[state-diagram.png]]
 Back: $F = \{q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643317-->
 END%%
 %%ANKI
 Basic
 What name is given to a finite automaton's standard graphical depiction?
 Back: Its state diagram.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643321-->
 END%%
 %%ANKI
 Cloze
 {1:Edges} are to {2:diagraphs} whereas {2:transitions} are to {1:state diagrams}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643325-->
 END%%
 %%ANKI
 Cloze
 {1:Vertices} are to {2:graphs} whereas {2:states} are to {1:state diagrams}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643328-->
 END%%
 %%ANKI
 Cloze
 The {final} states of a finite automaton are also called the {accept} states.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643332-->
 END%%
 If $s$ is processed by machine $M$ such that $M$ finishes in an accept state, we say $M$ **accepts** $s$. Otherwise $M$ **rejects** $s$. If $A$ is the set of all strings that $M$ accepts, we say that $A$ is the **language of machine $M$**, denoted $L(M) = A$. We say that $M$ **recognizes** $A$.
 %%ANKI
 Basic
 What does it mean for finite automaton $M$ to accept string $s$?
 Back: $M$ finishes processing $s$ on an accept state.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643336-->
 END%%
 %%ANKI
 Basic
 What does it mean for finite automaton $M$ to reject string $s$?
 Back: $M$ finishes processing $s$ on a non-accept state.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643342-->
 END%%
 %%ANKI
 Basic
 Let $M$ be a finite automaton. What is the language of $M$?
 Back: The set of strings $M$ accepts.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643347-->
 END%%
 %%ANKI
 Cloze
 Finite automaton $M$ {1:accepts} {2:strings} and {2:recognizes} {1:languages}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643352-->
 END%%
 %%ANKI
 Basic
 How is the language of finite automaton $M$ denoted?
 Back: As $L(M)$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643358-->
 END%%
 %%ANKI
 Basic
 Let $M$ be a finite automaton. What is $L(M)$ called?
 Back: The language of $M$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643364-->
 END%%
 %%ANKI
 Basic
 Let $M$ be a finite automaton. What kind of mathematical entity is $L(M)$?
 Back: A set (of strings).
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643370-->
 END%%
 %%ANKI
 Basic
 How many strings can a finite automaton potentially accept?
 Back: Zero or more.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643375-->
 END%%
 %%ANKI
 Basic
 How many languages can a finite automaton potentially recognize?
 Back: Exactly one.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643380-->
 END%%
 %%ANKI
 Basic
 Suppoe finite automaton $M$ does not accept any strings. What language does it recognize?
 Back: $\varnothing$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643385-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $Q$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $Q = \{q_1, q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643390-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\Sigma$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $\Sigma = \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643396-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $F$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $F = \{q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643402-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $q_0$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $q_0 = q_1$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643408-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\mathop{\text{dom}}\delta$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $\{q_1, q_2\} \times \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643415-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\mathop{\text{ran}}\delta$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $\{q_1, q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643420-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $L(M)$ evaluate to?
 ![[state-diagram-ends1.png]]
 Back: $\{w \mid w \text{ ends with a } 1 \}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643424-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $Q$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $Q = \{q_1, q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643428-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\Sigma$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $\Sigma = \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643433-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $F$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $F = \{q_1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643440-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $q_0$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $q_0 = q_1$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643445-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\mathop{\text{dom}}\delta$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $\{q_1, q_2\} \times \{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643450-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $\mathop{\text{ran}}\delta$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $\{q_1, q_2\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643455-->
 END%%
 %%ANKI
 Basic
 Consider finite automaton $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ below. What does $L(M)$ evaluate to?
 ![[state-diagram-ends0.png]]
 Back: $\{w \mid w = \epsilon \lor w \text{ ends with a } 0 \}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734999643459-->
 END%%
 %%ANKI
 Basic
 What is a regular language?
 Back: A language recognized by some finite automaton.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1735008834183-->
 END%%
 %%ANKI
 Cloze
 A {regular} language is a language {recognized by some finite automaton}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1735008834191-->
 END%%
 ## Bibliography
 * Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
--- a/notes/computability/images/state-diagram-ends0.png
+++ b/notes/computability/images/state-diagram-ends0.png
--- a/notes/computability/images/state-diagram-ends1.png
+++ b/notes/computability/images/state-diagram-ends1.png
--- a/notes/computability/images/state-diagram.png
+++ b/notes/computability/images/state-diagram.png
--- a/notes/computability/index.md
+++ b/notes/computability/index.md
@ -0,0 +1,3 @@
 ---
 title: Computability
 ---
--- a/notes/computability/language.md
+++ b/notes/computability/language.md
@ -0,0 +1,290 @@
 ---
 title: Language
 TARGET DECK: Obsidian::STEM
 FILE TAGS: language
 tags:
  - language
 ---
 ## Overview
 An **alphabet** is any nonempty finite set. The members of an alphabet are called **symbols** of the alphabet. A **string over an alphabet** is a finite sequence of symbols from that alphabet, usually written next to one another without separation.
 Then **length** of a string $w$ over an alphabet, denoted $\lvert w \rvert$, is the number of symbols $w$ contains. The **empty string**, denoted $\epsilon$, is the string of length $0$. The **reverse** of $w$ is the string obtained by writing $w$ in the opposite order.
 String $z$ is a **substring** of $w$ if $z$ appears consecutively within $w$. The **concatenation** of strings $x$ and $y$, written $xy$, is the string obtained by appending $y$ to the end of $x$. We say string $x$ is a **prefix** of string $y$ if a string $z$ exists where $xz = y$. We say $x$ is a **proper prefix** of $y$ if $x \neq y$.
 A **language** is a set of strings. A language is **prefix-free** if no member is a proper prefix of another member.
 %%ANKI
 Basic
 What is an alphabet?
 Back: A nonempty finite set.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366600-->
 END%%
 %%ANKI
 Basic
 An alphabet is a set satisfying what two properties?
 Back: It is nonempty and finite.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366604-->
 END%%
 %%ANKI
 Basic
 What is a symbol of an alphabet?
 Back: A member of the alphabet.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366608-->
 END%%
 %%ANKI
 Basic
 What name is given to members of an alphabet?
 Back: Symbols.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366611-->
 END%%
 %%ANKI
 Cloze
 A {symbol} is a {member} of an {alphabet}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366614-->
 END%%
 %%ANKI
 Basic
 What is a string over an alphabet?
 Back: A finite sequence of symbols from that alphabet.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366618-->
 END%%
 %%ANKI
 Basic
 What kind of mathematical entity is a string over an alphabet?
 Back: A finite sequence.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366621-->
 END%%
 %%ANKI
 Basic
 $01001$ is a string over what minimal alphabet?
 Back: $\{0, 1\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366624-->
 END%%
 %%ANKI
 Basic
 $hello$ is a string over what minimal alphabet?
 Back: $\{e, h, l, o\}$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366627-->
 END%%
 %%ANKI
 Basic
 How is the length of string $s$ over alphabet $\Sigma$ denoted?
 Back: As $\lvert s \rvert$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366630-->
 END%%
 %%ANKI
 Basic
 How is the length of a string over an alphabet defined?
 Back: As the number of symbols in the string.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366633-->
 END%%
 %%ANKI
 Basic
 Let $w$ be a string over some alphabet. How is the length of $w$ denoted?
 Back: $\lvert w \rvert$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366636-->
 END%%
 %%ANKI
 Basic
 What is the empty string over an alphabet?
 Back: The string of length $0$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366639-->
 END%%
 %%ANKI
 Basic
 How is the empty string over an alphabet typically denoted?
 Back: $\epsilon$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366642-->
 END%%
 %%ANKI
 Basic
 What is the reverse of string $w$ over some alphabet?
 Back: The string obtained by writing $w$ in opposite order.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366645-->
 END%%
 %%ANKI
 Basic
 How is the reverse of string $w$ over some alphabet typically denoted?
 Back: $w^R$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366648-->
 END%%
 %%ANKI
 Basic
 How does the length of a string relate to the length of its reverse?
 Back: They are equal.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366651-->
 END%%
 %%ANKI
 Basic
 How does the length of a string relate to the length of a substring?
 Back: The latter is less than or equal to the former.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366655-->
 END%%
 %%ANKI
 Basic
 What is a substring of string $w$ over some alphabet?
 Back: A string that appears consecutively within $w$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366659-->
 END%%
 %%ANKI
 Basic
 Let $x$ and $y$ be strings over some alphabet. How is their concatenation denoted?
 Back: $xy$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366662-->
 END%%
 %%ANKI
 Basic
 Let $x$ and $y$ be strings over some alphabet. What is the length of $\lvert x y \rvert$?
 Back: $\lvert x \rvert + \lvert y \rvert$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366666-->
 END%%
 %%ANKI
 Basic
 How is the concatenation of strings $x$ and $y$ over some alphabet denoted?
 Back: $xy$
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366671-->
 END%%
 %%ANKI
 Basic
 Let $x$ be a string over some alphabet. What does $xx$ denote?
 Back: The concatenation of $x$ with itself.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366675-->
 END%%
 %%ANKI
 Cloze
 Let $x$ be a string over some alphabet. Then {$xx$} $=$ {$x^2$}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366679-->
 END%%
 %%ANKI
 Basic
 Let $x$ be a string over some alphabet. What does $x^k$ denote?
 Back: The concatenation of $x$ with itself $k$ times.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366683-->
 END%%
 %%ANKI
 Basic
 What does it mean for string $x$ to be a prefix of string $y$ over some alphabet?
 Back: There exists some string $z$ such that $xz = y$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366687-->
 END%%
 %%ANKI
 Basic
 What does it mean for string $x$ to be a proper prefix of string $y$ over some alphabet?
 Back: There exists some string $z$ such that $xz = y$ and $x \neq y$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366692-->
 END%%
 %%ANKI
 Basic
 What does it mean for string $x$ to be a suffix of string $y$ over some alphabet?
 Back: There exists some string $z$ such that $zx = y$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366697-->
 END%%
 %%ANKI
 Basic
 What does it mean for string $x$ to be a proper suffix of string $y$ over some alphabet?
 Back: There exists some string $z$ such that $zx = y$ and $x \neq y$.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366702-->
 END%%
 %%ANKI
 Basic
 What is a language?
 Back: A nonempty set of strings.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366705-->
 END%%
 %%ANKI
 Basic
 A language is a set satisfying what?
 Back: It contains strings over some alphabet.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366709-->
 END%%
 %%ANKI
 Cloze
 {1:Symbols} are to {2:alphabets} whereas {2:strings} are to {1:languages}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366713-->
 END%%
 %%ANKI
 Basic
 What does it mean for a language to be prefix-free?
 Back: No member is a *proper* prefix of another member.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366717-->
 END%%
 %%ANKI
 Basic
 What does it mean for a language to be suffix-free?
 Back: No member is a *proper* suffix of another member.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366720-->
 END%%
 ## Bibliography
 * Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
--- a/notes/computability/regexp.md
+++ b/notes/computability/regexp.md
@ -8,6 +8,10 @@ tags:
 ## Overview
 TODO
 ## Extensions
 The following ERE (**E**xtended **R**egular **E**xpression) operators were defined to achieve consistency between programs like `grep`, `sed`, and `awk`. In POSIX, regexps are greedy.
 %%ANKI
@ -253,7 +257,7 @@ Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 202
 <!--ID: 1707050923713-->
 END%%
-## Character Classes
+### Character Classes
 Notation for describing a class of characters specific to a given locale/character set.
--- a/notes/data-models/index.md
+++ b/notes/data-models/index.md
@ -0,0 +1,3 @@
 ---
 title: Data Models
 ---
--- a/notes/data-models/rdf.md
+++ b/notes/data-models/rdf.md
@ -1,8 +1,9 @@
 ---
 title: RDF
 TARGET DECK: Obsidian::STEM
-FILE TAGS: ontology::rdf
+FILE TAGS: data_model::rdf
 tags:
  - data_model
  - rdf
 ---
@ -173,7 +174,7 @@ END%%
 Cloze
 RDF is a {data model} whereas XML is a {serialization}.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
-Tags: xml
+Tags: serialization::xml
 <!--ID: 1734805690321-->
 END%%
@ -182,7 +183,7 @@ Basic
 How might RDF and XML relate to one another?
 Back: XML can be used to serialize RDF.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
-Tags: xml
+Tags: serialization::xml
 <!--ID: 1734805690328-->
 END%%
--- a/notes/encoding/uri.md
+++ b/notes/encoding/uri.md
@ -1,8 +1,9 @@
 ---
 title: Uniform Resource Identifiers
 TARGET DECK: Obsidian::STEM
-FILE TAGS: uri
+FILE TAGS: encoding::uri
 tags:
  - encoding
  - uri
 ---
--- a/notes/posix/bash.md
+++ b/notes/posix/bash.md
@ -0,0 +1,204 @@
 ---
 title: Bash
 TARGET DECK: Obsidian::STEM
 FILE TAGS: bash
 tags:
  - bash
 ---
 ## Overview
 Bash, the Bourne-Again Shell, is a shell program and command language.
 %%ANKI
 Basic
 How do you escape a `'` within a single-quote string?
 Back: This is impossible.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752230-->
 END%%
 %%ANKI
 Basic
 What does the null string refer to?
 Back: The empty string, i.e. `""`.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752237-->
 END%%
 %%ANKI
 Basic
 When does Bash remove null strings from a command?
 Back: When they occur as part of a non-null command-line argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816752241-->
 END%%
 %%ANKI
 Basic
 Why does the following not work correctly?
 ```bash
 $ # -F specifies the field separator
 $ awk -F"" 'program' files
 ```
 Back: Bash removes the null string before executing the command.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706816764555-->
 END%%
 ## Prompts
 According to Robbins a POSIX-compliant shell (like Bash) generally has the primary and secondary prompts denoted with `$` and `>` respectively. Adjust these values using environment variables `$PS1` and `PS2` respectively.
 %%ANKI
 Basic
 What symbol is usually used to denote the primary prompt?
 Back: `$$`
 Reference:  Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706882670149-->
 END%%
 %%ANKI
 Basic
 What environment variable controls Bash's primary prompt?
 Back: `$$PS1`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706973587222-->
 END%%
 %%ANKI
 Basic
 What symbol is usually used to denote the secondary prompt?
 Back: `>`
 Reference:  Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706882670158-->
 END%%
 %%ANKI
 Basic
 What environment variable controls Bash's secondary prompt?
 Back: `$$PS2`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706973587232-->
 END%%
 Paths supplied to commands are typically "sanitized" by prefixing the path name with `./`. This is mentioned in a few different places:
 * `find -execdir` performs this prefixing automatically on all found files.
 * `awk` ambiguously interprets a file named e.g. `count=1` as variable assignment. Should write `$ awk -f program.awk ./count=1`.
 %%ANKI
 Basic
 What methodology is commonly used to "sanitize" paths supplied as command-line arguments?
 Back: Prefixing the paths with `./`.
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706885111460-->
 END%%
 ## Shebang
 The shebang (also writting shabang or sha-bang) is a magic character at the start of a script indicating what command should be run when invoking the script directly. It always begins with ASCII characters `#!`.
 %%ANKI
 Basic
 What ASCII characters do shebangs start with?
 Back: `#!`
 Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 <!--ID: 1706726911458-->
 END%%
 %%ANKI
 Basic
 What class of programs can be specified in a shebang?
 Back: Interpreters
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911461-->
 END%%
 %%ANKI
 Basic
 The OS will parse a shebang into what three parts?
 Back: `#!`, the interpreter, and the rest of the line as a single argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911464-->
 END%%
 %%ANKI
 Basic
 What gotcha does Robbins highlight with shebang parsing?
 Back: The remainder of the line following the interpreter is passed as a *single* argument.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911467-->
 END%%
 Some systems limit the length of interpreters to just 32 characters. A simple workaround when encountering this limitation is to introduce a symbolic link.
 %%ANKI
 Basic
 What workaround is used when shebang interpreter names are too long?
 Back: Introduce a symbolic link.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911470-->
 END%%
 ## Robustness
 An interesting point Robbins discusses in his introduction to [[posix/awk/index|gawk]] is this idea of command robustness. He states that:
 > A self-contained shell script is more reliable because there are no other files to misplace.
 %%ANKI
 Basic
 What is a self-contained shell script?
 Back: A shell script that does not rely on the presence of other files.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911473-->
 END%%
 %%ANKI
 Basic
 What makes a self-contained shell script more reliable?
 Back: There are no other files to misplace.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1706726911475-->
 END%%
 He argues that the first command below is more robust than the second since the command is more loosely coupled to its environment:
 ```bash
 $ awk 'program' input-file1 input-file2 ...
 $ awk -f program-file input-file1 input-file2 ...
 ```
 It's interesting to think what else can be used as a measure of a command's robustness:
 * Required environment variables or environment variables formatted in a certain way
 	* `$PATH` needs to point to a specific location
 * Whether the invoked program is present by default in a distribution or must be installed
 * The ability to run with or without an associated TTY
 * The ability to run with or without associated standard streams
 	* `stdout`, `stderr`, `stdin`
 * How backwards compatible the invoked program is
 	* Version mismatch may silently cause the same invocation to fail
 * Expected permissions
 	* EUID, read permissions on an input file, etc.
 * Determinism of the program itself
 	* Does output rely entirely on input or can it make nondeterministic choices
 * The amount of resources dedicated to the program
 	* Failure may occur if not enough memory is provided to the command
 * Whether a program acts idempotently
 	* What happens if I run the command twice in a row?
 * Whether a program acts atomically
 	* Is it possible intermediate files are left that affect subsequent runs?
 * The presence of timeouts
 	* Perhaps a program waits a specified amount of time before input is available. The command's success is now externally determined.
 * Locale-aware functionality
 	* Consider for instance [[posix/awk/index|gawk]]'s `\u` [[escape-sequences|sequence]] which targets characters in the current locale's character set as opposed to specifically Unicode.
 	* POSIX standard [[regexp#Character Classes|character classes]] serve as another example.
 The above scenarios are what makes something like nix so compelling.
 ## Bibliography
 * Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 * Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
--- a/notes/serialization/index.md
+++ b/notes/serialization/index.md
@ -0,0 +1,3 @@
 ---
 title: Serialization
 ---
--- a/notes/serialization/xml.md
+++ b/notes/serialization/xml.md
@ -1,8 +1,9 @@
 ---
 title: XML
 TARGET DECK: Obsidian::STEM
-FILE TAGS: xml
+FILE TAGS: serialization::xml
 tags:
  - serialization
  - xml
 ---