Answered: automaton is minimal by showing that no…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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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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