30 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Automaton | Obsidian::STEM | computability::automaton |
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Finite Automata
A finite automaton is a 5-tuple \langle Q, \Sigma, \delta, q_0, F \rangle, where
Qis a finite set called the states;\Sigmais a finite set called the alphabet;\delta \colon Q \times \Sigma \rightarrow Qis the transition function;q_0 \in Qis the start state; andF \subseteq Qis 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 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? 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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
END%%
%%ANKI
Basic
Consider diagram of finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle. What does Q evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider diagram of finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle. What does \Sigma evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider diagram of finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle. What does q_0 evaluate to?
!
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).
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?
!
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).
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?
!
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).
END%%
%%ANKI
Basic
Consider diagram of finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle. What does F evaluate to?
!
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).
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).
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%%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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does Q evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \Sigma evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does F evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does q_0 evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \mathop{\text{dom}}\delta evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \mathop{\text{ran}}\delta evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does L(M) evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does Q evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \Sigma evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does F evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does q_0 evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \mathop{\text{dom}}\delta evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does \mathop{\text{ran}}\delta evaluate to?
!
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).
END%%
%%ANKI
Basic
Consider finite automaton M = \langle Q, \Sigma, \delta, q_0, F \rangle below. What does L(M) evaluate to?
!
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).
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).
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).
END%%
%%ANKI Basic What is a nonregular language? Back: One that exists beyond the capabilities of a 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).
END%%
Regular Operations
Let A and B be languages. Then the regular operations union, intersection, concatenation, and Kleene star are defined as:
- Union:
A \cup B = \{x \mid x \in A \lor x \in B \} - Intersection:
A \cap B = \{x \mid x \in A \land x \in B\} - Concatenation:
A \circ B = \{ xy \mid x \in A \land y \in B \} - Kleene star:
A^* = \{ x_1x_2\cdots x_k \mid k \geq 0 \land x_i \in A \}
%%ANKI
Basic
Let A and B be languages. How is the union regular operation defined?
Back: As A \cup B = \{ x \mid x \in A \lor x \in B \}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. How is the intersection regular operation defined?
Back: As A \cap B = \{ x \mid x \in A \land x \in B \}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. How is the concatenation regular operation defined?
Back: As A \circ B = \{ xy \mid x \in A \land y \in B \}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A be a language. How is the Kleene star regular operation defined?
Back: As A^* = \{ x_1x_2 \cdots x_k \mid k \geq 0 \land x_1, \ldots, x_k \in 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).
END%%
%%ANKI
Basic
Let A and B be languages. How is their union denoted?
Back: A \cup B
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. How is their intersection denoted?
Back: A \cap B
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. How is their concatenation denoted?
Back: A \circ B
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A be a language. How is its Kleene star denoted?
Back: 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).
END%%
%%ANKI Basic Why are the regular operations named the way they are? Back: Because the set of regular languages is closed under them. Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A = \{a, b \} and B = \{c, d\} be languages. What does A \cup B evaluate to?
Back: \{a, b, c, d\}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A = \{a, b \} and B = \{c, d\} be languages. What does A \cap B evaluate to?
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).
END%%
%%ANKI
Basic
Let A = \{a, b \} and B = \{c, d\} be languages. What does A \circ B evaluate to?
Back: \{ac, ad, bc, bd\}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A = \{a, b \} be a language. What does A^* evaluate to?
Back: \{\epsilon, a, b, aa, ab, ba, bb, \ldots\}
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A be a language. What regular operation is denoted as A^*?
Back: The Kleene star.
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. What regular operation is denoted as A \cup B?
Back: The union.
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. What regular operation is denoted as A \cap B?
Back: The intersection.
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
END%%
%%ANKI
Basic
Let A and B be languages. What regular operation is denoted as A \circ B?
Back: The concatenation.
Reference: Michael Sipser, Introduction to the Theory of Computation, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
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).