8 Regular Languages and Finite Automata (AMP) (a) (i) Given any non-deterministic finite automaton M, describe how to construct a regular expression r whose language of matching strings L(r) is equal to the language L(M) accepted by M. (ii) Give a regular expression r with L(r) = L(M) when M is the following non-deterministic finite automaton. 1 2 (b) State the Pumping Lemma and explain how it is used to prove that languages are not regular. (c) Are the following languages regular? Justify your answer in each case. (i) L₁= {akbmcn | (k = m or m = n) and k +m+n>2} (ii) L₂ = {akbmcn | (k = m or m = n) and k + m + n ≤ 2} (iii) L3 = {akbmcn | k+m+n>2}
8 Regular Languages and Finite Automata (AMP) (a) (i) Given any non-deterministic finite automaton M, describe how to construct a regular expression r whose language of matching strings L(r) is equal to the language L(M) accepted by M. (ii) Give a regular expression r with L(r) = L(M) when M is the following non-deterministic finite automaton. 1 2 (b) State the Pumping Lemma and explain how it is used to prove that languages are not regular. (c) Are the following languages regular? Justify your answer in each case. (i) L₁= {akbmcn | (k = m or m = n) and k +m+n>2} (ii) L₂ = {akbmcn | (k = m or m = n) and k + m + n ≤ 2} (iii) L3 = {akbmcn | k+m+n>2}
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
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Transcribed Image Text:8 Regular Languages and Finite Automata (AMP)
(a) (i) Given any non-deterministic finite automaton M, describe how to construct
a regular expression r whose language of matching strings L(r) is equal to
the language L(M) accepted by M.
(ii) Give a regular expression r with L(r)
non-deterministic finite automaton.
1
a
a
(2)
=
L(M) when M is the following
(b) State the Pumping Lemma and explain how it is used to prove that languages
are not regular.
(c) Are the following languages regular? Justify your answer in each case.
(i) L₁ = {akbmcn | (k = m or m = n) and k + m + n ≥ 2}
(ii) L₂= {akbmen | (k = m or m = n) and k +m+n≤ 2}
(iii) L3 = {akbmcn|k+m+n≥2}
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