automaton is minimal by showing that no determistic finite automaton
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter17: Markov Chains
Section17.4: Classification Of States In A Markov Chain
Problem 3P
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Please answer part 3 of this question.
Let Σ = {0, 1} and consider the following language L = {w ∈ Σ∗ : w contains the substring 10 or 01}.
1. Give a minimal deterministic finite automaton M accepting L.
2. Provide a “proof sketch” which shows the correctness of your automaton. To do this:
a. Make a claim about your machine’s extended transition function δ∗. You do not need to prove your claim.
b. Show, using your claim, that L(M) = L.
3. Show that your automaton is minimal by showing that no determistic finite automaton, N, can exist such that L(N) = L and N has fewer states than M.
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