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We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
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The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat
Let L1 and L2 be CGF. We show that L1 ∩ L2 is CFG too. Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the sec
Question 2 (10 pt): In this question we look at an extension to DFAs. A composable-reset DFA (CR-DFA) is a five-tuple, (Q,S,d,q0,F) where: – Q is the set of states, – S is the alph
The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
how many pendulum swings will it take to walk across the classroom?
The Myhill-Nerode Theorem provided us with an algorithm for minimizing DFAs. Moreover, the DFA the algorithm produces is unique up to isomorphism: every minimal DFA that recognizes
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