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5. (20 pt.) Prove that the class of regular languages is closed under reverse. That is,...
(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.
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.]
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.
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
Question 1: Every language is regular T/F Question 2: There exists a DFA that has only one final state T/F Question 3: Let M be a DFA, and define flip(M) as the DFA which is identical to M except you flip that final state. Then for every M, the language L(M)^c (complement) = L( flip (M)). T/F Question 4: Let G be a right linear grammar, and reverse(G)=reverse of G, i.e. if G has a rule A -> w B...
Question 8, please. 2. Prove: (a) the set of even numbers is countable. (b i=1 3. The binary relation on pair integers - given by (a,b) - (c,d) iff a.d=cbis an equivalence relation. 4. Given a graph G = (V, E) and two vertices s,t EV, give the algorithm from class to determine a path from s to t in G if it exists. 5. (a) Draw a DFA for the language: ( w w has 010 as a substring)....
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
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. 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.