◆ For regular languages, we can use any of its representations to prove a closure property.Īnswer: The class of languages recognized by NFAs is closed under complement, which we can prove as follows. Recall a closure property is a statement that a certain operation on languages, when applied to languages in a class (e.g., the regular languages), produces a result that is also in that class. Lets first draw the DFA for L1 that accepts the strings of even length. The language accepted by the complemented DFA L2 is the complement of the language L1. The complement of a DFA can be obtained by making the non-final states as final states and vice-versa. To see this fact, take deterministic FA for L and interchange the accept and reject states. The statement says that if L is a regular lan- guage, then so is L. The complement of language L, written L, is all strings not in L but with the same alphabet. The set of regular languages is closed under complementation. Why are languages closed under complementation? Because there are Turing reductions from every problem to its complement, any class which is closed under Turing reductions is closed under complement. Which one is the complement of the below NFA?Ī class is said to be closed under complement if the complement of any problem in the class is still in the class.Which of the operations are closed under regular expression?. Why are languages closed under complementation?.On eac.ħ.7.34: Recall, in our discussion of the ChurchTuring thesis, that we intro.ħ.7.35: A subset of the nodes of a graph G is a dominating set if every oth.ħ.7.36: Show that thefollowingproblem is NP-complete. ħ.7.32: This problem is inspired by the single-player game Minesweeper, gen.ħ.7.33: In the following solitaire game, you are given an m m board. ħ.7.31: Consider the following scheduling problem. ħ.7.4: Fill out the table described in the polynomial time algorithm for c.ħ.7.5: Is the following formula satisable?(x y) (x y) (x y) (x y)ħ.7.6: Show that P is closed under union, concatenation, and complement.ħ.7.7: Show that NP is closed under union and concatenation.ħ.7.8: Let CONNECTED = is. 2n.ħ.7.3: Which of the following pairs of numbers are relatively prime? Show.
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