(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression: 2, r'-0. ((r*). r), i-, +½. (b) Given a regular expression i = a(ab)* +b°a*, r, = (b + a) * +a*, find L(;) and L(r,), the languages associated with 7i and r2, respective ly. (c) Find a regular expression r such that L(r) is the same as L= {b"ab",(ba)*: n, m2 0,h2 1}.

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
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(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s:
2, r'-0. ((r')). r), n -n +½.
(b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,),
the languages associated with i and r3, respective ly.
(c) Find a regular expression r such that L(r) is the same as
L = {b"ab",(ba)* : n, m2 0,h2 1}.
%3D
Transcribed Image Text:(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s: 2, r'-0. ((r')). r), n -n +½. (b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,), the languages associated with i and r3, respective ly. (c) Find a regular expression r such that L(r) is the same as L = {b"ab",(ba)* : n, m2 0,h2 1}. %3D
Expert Solution
Step 1

a) λ, r*Φ, r1-r2+r3

b) L(r1) = {a(ab)n | n>=0} U {bman | m>0,n>0}

L(r2) = {(bnam)k | m,n,k>0} U {am | m>0}

c) r = b*ab*+(ba)+

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