Reorganize finite automata. Flashcard fixups.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -226,7 +226,15 @@
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-  "Added Media": [],
+  "Added Media": [
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+    "dfa-ends1.png",
+    "dfa-ends0.png",
+    "schroder-bernstein.png",
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+    "complex-plane-point.png"
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@@ -902,7 +910,7 @@
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@@ -954,7 +962,7 @@
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-    "set/cardinality.md": "a684ba2638e90d6d5647054230b3f35f",
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@@ -1014,7 +1022,7 @@
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     "_journal/2024-12/2024-12-15.md": "be66c8808d8bb66d4e7b91db7c93c94a",
     "linkers/elf.md": "0734c90bf5b09319ae1f3bdd965de1c1",
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@@ -1029,7 +1037,7 @@
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     "encoding/xml/index.md": "01a66b1a102cccc682f8f1cab0f50bc6",
-    "ontology/reification.md": "8b51f0583bed52a366f2b1fe9608d094",
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     "ontology/rdf.md": "fd273c30bec6f46b68547f0d392620b1",
     "data-models/rdf.md": "4aa5af33cc8badada41ca165e05b1381",
     "serialization/xml.md": "84b632282ebcc2b6216923a02abdd4c2",
@@ -1038,7 +1046,7 @@
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     "formal-system/language.md": "7797d33a0b0eb187d43dda46a138fb25",
-    "computability/automaton.md": "adebd457532a94c801221e128e92decc",
+    "computability/automaton.md": "fbcaa13a3e2053f252c58f0662fe7ada",
     "computability/index.md": "d7938428ed0b0224c1fe1e59d1fab118",
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@@ -1049,13 +1057,13 @@
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-    "linkers/relocatable.md": "58d45ac26d43c765b33cb9f88823a5ea",
+    "linkers/relocatable.md": "b6f0c13e07ed57ea73dea6b4a72560d1",
     "data-models/federation.md": "1d92747304186bd2833a00a488fcac48",
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     "_journal/2024-12/2024-12-26.md": "59e59cad1ae568adbe8e27e98d36c59c",
-    "combinators/index.md": "ca8ed1ce82da585b908e06c2b457922d",
+    "combinators/index.md": "8e324bbcf49cca9c0c0f9bbf843cbebb",
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@@ -1403,7 +1411,7 @@
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     "_journal/2025-01/2025-01-01.md": "3cf29f753c27313c95a435a7845b4c13",
-    "algebra/complex.md": "37befb93643418cd8905c49e2f53627b",
+    "algebra/complex.md": "56cb9e1f6da0fe1e75f750709a35803f",
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@@ -1420,7 +1428,7 @@
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notes/algebra/complex.md

@@ -14,7 +14,7 @@ where $i$ is the **imaginary number** defined as $i^2 = -1$.
 
 %%ANKI
 Basic
-How is set the complex numbers denoted?
+How is the set of complex numbers denoted?
 Back: As $\mathbb{C}$.
 Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh edition, Pearson new international edition (Harlow: Pearson, 2014).
 <!--ID: 1735870487309-->
@@ -76,7 +76,7 @@ Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh editi
 END%%
 
 %%ANKI
-Cloze
+Basic
 What real number is identified with $-\pi + 0i$?
 Back: $-\pi$
 Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh edition, Pearson new international edition (Harlow: Pearson, 2014).
@@ -84,7 +84,7 @@ Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh editi
 END%%
 
 %%ANKI
-Cloze
+Basic
 What real number is identified with $\pi + 2i$?
 Back: N/A.
 Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh edition, Pearson new international edition (Harlow: Pearson, 2014).

notes/algorithms/dfs.md

@@ -584,7 +584,7 @@ END%%
 
 %%ANKI
 Basic
-Let $v$ be black when $\langle u, v \rangle$ is explored. If $u.d < v.d$, what kind of edge is $\langle u, v \rangle$ classified as?
+Let $v$ be black when $\langle u, v \rangle$ is explored. If $u{.}d < v{.}d$, what kind of edge is $\langle u, v \rangle$ classified as?
 Back: A forward edge.
 Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
 <!--ID: 1735785232475-->
@@ -592,7 +592,7 @@ END%%
 
 %%ANKI
 Basic
-Let $v$ be black when $\langle u, v \rangle$ is explored. If $v.d < u.d$, what kind of edge is $\langle u, v \rangle$ classified as?
+Let $v$ be black when $\langle u, v \rangle$ is explored. If $v{.}d < u{.}d$, what kind of edge is $\langle u, v \rangle$ classified as?
 Back: A cross edge.
 Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
 <!--ID: 1735785232480-->

notes/c17/strings/printf.md

@@ -683,7 +683,7 @@ END%%
 %%ANKI
 Basic
 How does `%g` handle non-integral values differently from `%f`?
-Back: It excludes insignifant `0`s after the decimal point.
+Back: It excludes insignificant `0`s after the decimal point.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 <!--ID: 1710603411174-->
 END%%

notes/combinators/index.md

@@ -235,7 +235,7 @@ END%%
 %%ANKI
 Basic
 In a combinatory logic system, what is a combinator?
-Back: A closed term with no atomic constants.
+Back: A closed term with no atomic constants (besides the basic combinators).
 Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
 <!--ID: 1735413657662-->
 END%%

notes/computability/automaton.md

@@ -7,275 +7,22 @@ tags:
   - computability
 ---
 
-## Finite Automata
+## Overview
 
-A **finite automaton** is a $5$-tuple $\langle Q, \Sigma, \delta, q_0, F \rangle$, where
+**Finite automata** are classified as either **deterministic** or **nondeterministic**. These two representations are equivalent.
 
-1. $Q$ is a finite set called the **states**;
+If $s$ is processed by finite automaton $M$ 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** $A$.
-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.
+A [[computability/index|language]] is called a **regular language** if a finite automaton recognizes it.
-
-![[state-diagram.png]]
-
-A [[language]] is called a **regular language** if a finite automaton recognizes it.
 
 %%ANKI
 Basic
-A finite automaton is defined as a tuple of how many components?
+Finite automaton are largely classified in what two buckets?
-Back: Five.
+Back: Deterministic and nondeterministic.
 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-->
+<!--ID: 1736721887587-->
 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: $q_0 \in Q$
-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:graphs} 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 $s$?
@@ -349,138 +96,12 @@ END%%
 
 %%ANKI
 Basic
-Suppoe finite automaton $M$ does not accept any strings. What language does it recognize?
+Suppose 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?
@@ -504,6 +125,405 @@ Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third ed
 <!--ID: 1735160593029-->
 END%%
 
+## Determinism
+
+A **deterministic finite automaton** (DFA) 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.
+
+![[dfa-example.png]]
+
+%%ANKI
+Basic
+A deterministic finite automaton is defined as a tuple 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
+What is DFA an acronym for?
+Back: **D**eterministic **f**inite **a**utomata.
+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: 1736721887614-->
+END%%
+
+%%ANKI
+Basic
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. How does $q_0$ relate to $Q$?
+Back: $q_0 \in Q$
+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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M$ be a DFA. 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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $Q$ evaluate to?
+![[dfa-example.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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\Sigma$ evaluate to?
+![[dfa-example.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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $q_0$ evaluate to?
+![[dfa-example.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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{dom}}\delta$ evaluate to?
+![[dfa-example.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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{ran}}\delta$ evaluate to?
+![[dfa-example.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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $F$ evaluate to?
+![[dfa-example.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 DFA'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:graphs} 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 DFA 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%%
+
+%%ANKI
+Basic
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $Q$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\Sigma$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $F$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $q_0$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{dom}}\delta$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{ran}}\delta$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $L(M)$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $Q$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\Sigma$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $F$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $q_0$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{dom}}\delta$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $\mathop{\text{ran}}\delta$ evaluate to?
+![[dfa-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
+Let $M = \langle Q, \Sigma, \delta, q_0, F \rangle$ be the depicted DFA. What does $L(M)$ evaluate to?
+![[dfa-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%%
+
 ## Regular Operations
 
 Let $A$ and $B$ be languages. Then the **regular operations** union, intersection, concatenation, and Kleene star are defined as:

notes/linkers/relocatable.md

@@ -602,7 +602,7 @@ END%%
 %%ANKI
 Basic
 Linking fails at symbol resolution if what set(s) are nonempty?
-Back: Either the set of unresolved symbols or relocatable object files.
+Back: The set of unresolved symbols.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1736632025912-->
 END%%
@@ -620,7 +620,7 @@ Basic
 Let `p.o` depends on `libx.a`. What minimal command lets `cc` resolve all symbol references?
 Back:
 ```bash
-$ cc p.o -x
+$ cc p.o -lx
 ```
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1736632025920-->
@@ -631,7 +631,7 @@ Basic
 Let `p.o` depends on `liby.a` which depends on `libx.a` . What minimal command lets `cc` resolve all symbol references?
 Back:
 ```bash
-$ cc p.o -y -x
+$ cc p.o -ly -lx
 ```
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1736632025924-->

notes/ontology/reification.md

@@ -59,7 +59,7 @@ END%%
 
 %%ANKI
 Basic
-What "form" of reification does the following sentence take on? $$\text{Wikipedia says Shakespeare wrote Hamlet.}$$
+What "form(s)" of reification does the following sentence take on? $$\text{Wikipedia says Shakespeare wrote Hamlet.}$$
 Back: Provenance.
 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.
 <!--ID: 1734385502435-->
@@ -75,7 +75,7 @@ END%%
 
 %%ANKI
 Basic
-What "form" of reification does the following sentence take on? $$\text{It is 90\% probable that Shakespeare wrote Hamlet.}$$
+What "form(s)" of reification does the following sentence take on? $$\text{It is 90\% probable that Shakespeare wrote Hamlet.}$$
 Back: Likelihood.
 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.
 <!--ID: 1734385502443-->
@@ -91,7 +91,7 @@ END%%
 
 %%ANKI
 Basic
-What "form" of reification does the following sentence take on? $$\text{Kenneth Branagh played Hamlet in the movie.}$$
+What "form(s)" of reification does the following sentence take on? $$\text{Kenneth Branagh played Hamlet in the movie.}$$
 Back: Context.
 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.
 <!--ID: 1734385502453-->
@@ -107,7 +107,7 @@ END%%
 
 %%ANKI
 Basic
-What "form" of reification does the following sentence take on? $$\text{Hamlet plays on Broadway Jan. 11th through Mar. 12th.}$$
+What "form(s)" of reification does the following sentence take on? $$\text{Hamlet plays on Broadway Jan. 11th through Mar. 12th.}$$
 Back: Time frame.
 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.
 <!--ID: 1734385502463-->

notes/set/cardinality.md

@@ -493,14 +493,6 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1733407760105-->
 END%%
 
-%%ANKI
-Basic
-According to Enderton, what is the "essential demand" for defining cardinal numbers?
-Back: Defining cardinal numbers such that for any sets $A$ and $B$, $\mathop{\text{card}} A = \mathop{\text{card}} B$ iff $A \approx B$.
-Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
-<!--ID: 1733407760108-->
-END%%
-
 %%ANKI
 Basic
 What name is given to $\mathop{\text{card}} \omega$?
@@ -726,7 +718,7 @@ END%%
 %%ANKI
 Basic
 Let $K$ and $L$ be disjoint sets. What does $\mathop{\text{card}}(K \cup L)$ evaluate to?
-Back: As $\kappa + \lambda$ where $\kappa = \mathop{\text{card}} K$ and $\lambda = \mathop{\text{card}} L$.
+Back: $\mathop{\text{card}}K + \mathop{\text{card}}L$
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1733710439142-->
 END%%
@@ -873,14 +865,14 @@ END%%
 %%ANKI
 Basic
 Let $K$ and $L$ be sets. What does $\mathop{\text{card}}(K \times L)$ evaluate to?
-Back: As $\kappa \cdot \lambda$ where $\kappa = \mathop{\text{card}} K$ and $\lambda = \mathop{\text{card}} L$.
+Back: $\mathop{\text{card}}K \cdot \mathop{\text{card}}L$
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1733710439156-->
 END%%
 
 %%ANKI
 Basic
-Let $K \approx \kappa$ and $L \approx \lambda$. What is necessary for $\mathop{\text{card}}(K \times L) \approx \kappa \cdot \lambda$?
+Let $\mathop{\text{card}}K = \kappa$ and $\mathop{\text{card}}L = \lambda$. What is necessary for $\mathop{\text{card}}(K \times L) = \kappa \cdot \lambda$?
 Back: N/A. This is true by definition.
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1733710439159-->
@@ -1067,7 +1059,7 @@ END%%
 %%ANKI
 Basic
 Let $K$ and $L$ be sets. What does $\mathop{\text{card}}(^LK)$ evaluate to?
-Back: As $\kappa^\lambda$ where $\kappa = \mathop{\text{card}} K$ and $\lambda = \mathop{\text{card}} L$.
+Back: To $\kappa^\lambda$ where $\kappa = \mathop{\text{card}} K$ and $\lambda = \mathop{\text{card}} L$.
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1733710439168-->
 END%%