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The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is
(A, aabbba)
The ID after the ?rst three transitions of the computation is
(F, bba)
The progress of a computation involves a series of steps, each transforming an ID into its successor-consuming the next symbol of the input, following the corresponding edge and updating the state accordingly.
Exercise: Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.
Another striking aspect of LTk transition graphs is that they are generally extremely ine?cient. All we really care about is whether a path through the graph leads to an accepting
conversion from nfa to dfa 0 | 1 ___________________ p |{q,s}|{q} *q|{r} |{q,r} r |(s) |{p} *s|null |{p}
turing machine for prime numbers
Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL
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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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Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
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