3. Let D = (Q, Σ, 6, qo, I') be a DFA. Construct a new DFA D' from D such thatL(D') = {w € Σ* : wß = L(D) for some ß € [*},i.e., L(D') contains every string w that is a prefix of some string in L(D). (Hint: Try tomodify the set I of accept states in D.) Prove the correctness of your construction.

Answered: 3. Let D = (Q, E, 6, go, I) be a DFA.…

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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3. Let D = (Q, Σ, 6, qo, I') be a DFA. Construct a new DFA D' from D such that
L(D') = {w € Σ* : wß = L(D) for some ß € [*},
i.e., L(D') contains every string w that is a prefix of some string in L(D). (Hint: Try to
modify the set I of accept states in D.) Prove the correctness of your construction.

Expert Solution

Step 1: DFA

DFA stands for Deterministic Finite Automata. It is a 5-tuple,

, $M = (Q, ⅀, δ, q_{0}, F) w h e r e Q : f i n i t e n o n e m p t y s t a t e s ⅀ : F i n i t e n o n e m p t y s e t o f i n p u t s δ : T r a n s i t i o n f u n c t i o n q_{0} : I n i t i a l s t a t e F : s e t o f f i n a l s t a t e s$

In simple terms, every state must have a transition on each input symbol.

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