[Solved]10 Seen Given Dfa M N States Whether L M Infinite Decided P Time Basically Look State Q E Q37293703

10. You have seen that, given a DFA M of n states, whether L(M) is infinite can be decided in P-time: You basically look for a state q E Q(M) such that (1) there is a path from go to q, and also a path from q to some final state in M, and (2) there is a directed cycle having at least one edge (including a loop) from q back to q There is also a non-efficient algorithm that looks for all strings r of length n 1×1 < 2n such that z E L(M). Prove that this algorithm is also correct, but it takes exponential time. Now suppose you are given an NFA N. One way to decide whether L(N) is infinite is to first convert N to a DFA M. However this may take exponential time in the size of N. Design an algorithm that works directly for N, and prove that your algorithm is correct, and runs in polynomial time. Show transcribed image text 10. You have seen that, given a DFA M of n states, whether L(M) is infinite can be decided in P-time: You basically look for a state q E Q(M) such that (1) there is a path from go to q, and also a path from q to some final state in M, and (2) there is a directed cycle having at least one edge (including a loop) from q back to q There is also a non-efficient algorithm that looks for all strings r of length n 1×1

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Answer to 10. You have seen that, given a DFA M of n states, whether L(M) is infinite can be decided in P-time: You basically look… . . .