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Finite automata and consolidate bash/POSIX.

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Joshua Potter 2024-12-23 20:32:13 -07:00
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---
title: "2024-12-21"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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---
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.

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---
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]].

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---
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.).

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%%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%%

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---
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%%

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---
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)

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---
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)

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---
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)

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---
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).

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---
title: Intervals
TARGET DECK: Obsidian::STEM
FILE TAGS: calculus::intervals
FILE TAGS: calculus::interval
tags:
- calculus
---

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---
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).

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---
title: Computability
---

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---
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).

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## 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.

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---
title: Data Models
---

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---
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%%

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---
title: Uniform Resource Identifiers
TARGET DECK: Obsidian::STEM
FILE TAGS: uri
FILE TAGS: encoding::uri
tags:
- encoding
- uri
---

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---
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)

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---
title: Serialization
---

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---
title: XML
TARGET DECK: Obsidian::STEM
FILE TAGS: xml
FILE TAGS: serialization::xml
tags:
- serialization
- xml
---