1, 2, 3, 6, 7, 11. == Page 102 (You are asked to find regular grammar in questions 2, 6, 7, 11. To do so, find the NFA first, then each edge in the NFA gives a production in the regular grammar

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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Do ONLY: 1, 2, 3, 6, 7, 11. == Page 102 (You are asked to find regular grammar in questions 2, 6, 7, 11. To do so, find the NFA first, then each edge in the NFA gives a production in the regular grammar).

1. Construct a dfa that accepts the language generated by the grammar
S→ abA,
A→ baB,
B→ aAbb.
2. Find a regular grammar that generates the language L (aa* (ab+ a)*).
3. Construct a left-linear grammar for the language in Exercise 1.
4. Construct right- and left-linear grammars for the language
L = {a"b™ : n> 2, m² 3}.
5. Adapt the construction in Theorem 3.4 to find a left-linear grammar for the language accepted by
the nfa below.
6. Construct a right-linear grammar for the language L ((aab*ab)*).
7. Find a regular grammar that generates the language on E = {a, b} consisting of all strings with no
more than three a's.
8. In Theorem 3.5, prove that L(G) = (L(G))*.
9. Suggest a construction by which a left-linear grammar can be obtained from an nfa directly.
10. Find a left-linear grammar for the language in Exercise 6.
11. Find a regular grammar for the language L = {a"b™ : n + m is even}.
Transcribed Image Text:1. Construct a dfa that accepts the language generated by the grammar S→ abA, A→ baB, B→ aAbb. 2. Find a regular grammar that generates the language L (aa* (ab+ a)*). 3. Construct a left-linear grammar for the language in Exercise 1. 4. Construct right- and left-linear grammars for the language L = {a"b™ : n> 2, m² 3}. 5. Adapt the construction in Theorem 3.4 to find a left-linear grammar for the language accepted by the nfa below. 6. Construct a right-linear grammar for the language L ((aab*ab)*). 7. Find a regular grammar that generates the language on E = {a, b} consisting of all strings with no more than three a's. 8. In Theorem 3.5, prove that L(G) = (L(G))*. 9. Suggest a construction by which a left-linear grammar can be obtained from an nfa directly. 10. Find a left-linear grammar for the language in Exercise 6. 11. Find a regular grammar for the language L = {a"b™ : n + m is even}.
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