Answered: Think about the concept of extended…

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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Think about the concept of extended transition functions δ^* and ∆^* of Deterministic Finite Automata and Nondeterministic Finite Automata respectively. Prove the following facts about those functions using mathematical induction.

1. Given a DFA M = (Q, Σ, δ, s₀, F) and strings x, y ∈ Σ^*, we have δ^*(q, xy) = δ^*(δ^*(q, x), y).

2. Given a NFA N = (Q, Σ, ∆, S₀, F), subsets A ⊆ Q, B ⊆ Q and a string x ∈ Σ^∗, we have ∆* (A ∪ B, x) = ∆*(A, x) ∪ ∆*(B, x).

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