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).

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
icon
Related questions
Question

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**(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).

Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Dynamic Multithreading
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education