Prove that the class of regular languages is closed under intersection. That is, show that if...
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Prove that the class of regular languages is closed under intersection. That is, show
that if ? and ? are regular languages, then ? ∩ ? = {? | ? ∈ ? ??? ? ∈ ?} is also regular.
Hint:givenaDFA? =(?,Σ,?,?,?)thatrecognizes?andaDFA? =(?,Σ,?,?,?)that11111 22222
recognizes ?, construct a new DFA ? = (?, Σ, ?, ?0, ?) that recognizes ? ∩ ? and justify why your construction is correct.
Homework Answers
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Prove that the class of regular languages is closed under
intersection. That is, show
that if...
(20 pt.) Prove that the class of regular languages is closed under reverse. That is, show...
(20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR WE A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
5. (20 pt.) Prove that the class of regular languages is closed under reverse. That is,...
5. (20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR W E A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
Problem 3 [20 points Prove that the class of regular languages is closed under reverse. That...
Problem 3 [20 points Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR -[wR | w e A is also regular. [Hint: given a DFA M = (Q,Σ, δ, q0,F) that recognizes A, construct a new NFA (Q', Σ,8,6, F') that recognizes AR.]
Show using a cross-product construction that the class of regular languages is closed under set difference....
Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.
Show using a cross-product construction that the class of regular languages is closed under set difference....
Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.
2. (15) Show using a cross-product construction that the class of regular languages is closed under...
2. (15) Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.
Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection...
Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable lanquages are closed under union and intersection The class of undecidable languages contains the class of recognizable anguages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all that apply) 1 point EDFA-{ «A> 1 A is a DFA and...
1. (Non-regular languages) Prove that the following languages are not regular. You may use the pumping...
1. (Non-regular languages) Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, complement, and reverse (b) L2 = { w | w ∈ {0, 1}* is not a palindrome }. A palindrome is a string that reads the same forward and backward
Prove that the following languages are not regular. You may use the pumping lemma and the...
Prove that the following languages are not regular. You may use
the pumping lemma and the closure of the class of regular languages
under union, intersection, and compliment.
a){}
b){}
c) {
is not a palindrome}
*d)}
0"1"0" m,n>0
Automata Prove that regular languages are closed under difference, using an indirect proof (leveraging the closure...
Automata Prove that regular languages are closed under difference, using an indirect proof (leveraging the closure of other set operators).
(20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR WE A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
5. (20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR W E A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
Problem 3 [20 points Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR -[wR | w e A is also regular. [Hint: given a DFA M = (Q,Σ, δ, q0,F) that recognizes A, construct a new NFA (Q', Σ,8,6, F') that recognizes AR.]
Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.
2. (15) Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.
Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable lanquages are closed under union and intersection The class of undecidable languages contains the class of recognizable anguages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all that apply) 1 point EDFA-{ «A> 1 A is a DFA and...
Prove that the following languages are not regular. You may use
the pumping lemma and the closure of the class of regular languages
under union, intersection, and compliment.
a){}
b){}
c) {
is not a palindrome}
*d)}
0"1"0" m,n>0
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