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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Let r, s, and t be regular expressions over = { a , b } . In 28—30, determine whether the two regular expressions define the same language. If they do, describe the language. If they do not, give an example of a string that is in one of the languages but not the other.

28. ( r / s ) t and r t | s t

To determine

Let r,s and t be regular expressions over ={a,b}. Determine whether the two regular

expressions define the same language. If they do, describe the language. If they do not, give

an example of a string that is in one of the languages but not the other.

(r|s)tandrt|st

Explanation

Given information:

r,s,t be the regular expression.

Concept used:

Here (a,b)* represents any string at all made up of a'sandb's, this part is followed

by ab which is followed by any one of the expression aa,ab,baorbb.

Calculation:

The alphabet ={a,b,c} is defined over the regular expressions r,sandt.

Two regular expressions rand s are equivalent iff L(r)=L(s).

Use the following definitions:

Recursion: L(r|r')=L(r)L(r')andL(rr')=L(r)L(r')

Now check whether L((rs)t)=L(rtst) as follows:

L(( r|s)t)=L(r|s)L(t)=(L(r)L(s))L(t)={xy|xL(r)L(s)and yL(t)}={xy|(xL( r)or

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Chapter 12 Solutions

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Sect-12.1 P-11TYSect-12.1 P-12TYSect-12.1 P-1ESSect-12.1 P-2ESSect-12.1 P-3ESSect-12.1 P-4ESSect-12.1 P-5ESSect-12.1 P-6ESSect-12.1 P-7ESSect-12.1 P-8ESSect-12.1 P-9ESSect-12.1 P-10ESSect-12.1 P-11ESSect-12.1 P-12ESSect-12.1 P-13ESSect-12.1 P-14ESSect-12.1 P-15ESSect-12.1 P-16ESSect-12.1 P-17ESSect-12.1 P-18ESSect-12.1 P-19ESSect-12.1 P-20ESSect-12.1 P-21ESSect-12.1 P-22ESSect-12.1 P-23ESSect-12.1 P-24ESSect-12.1 P-25ESSect-12.1 P-26ESSect-12.1 P-27ESSect-12.1 P-28ESSect-12.1 P-29ESSect-12.1 P-30ESSect-12.1 P-31ESSect-12.1 P-32ESSect-12.1 P-33ESSect-12.1 P-34ESSect-12.1 P-35ESSect-12.1 P-36ESSect-12.1 P-37ESSect-12.1 P-38ESSect-12.1 P-39ESSect-12.1 P-40ESSect-12.1 P-41ESSect-12.2 P-1TYSect-12.2 P-2TYSect-12.2 P-3TYSect-12.2 P-4TYSect-12.2 P-5TYSect-12.2 P-6TYSect-12.2 P-7TYSect-12.2 P-8TYSect-12.2 P-9TYSect-12.2 P-10TYSect-12.2 P-1ESSect-12.2 P-2ESSect-12.2 P-3ESSect-12.2 P-4ESSect-12.2 P-5ESSect-12.2 P-6ESSect-12.2 P-7ESSect-12.2 P-8ESSect-12.2 P-9ESSect-12.2 P-10ESSect-12.2 P-11ESSect-12.2 P-12ESSect-12.2 P-13ESSect-12.2 P-14ESSect-12.2 P-15ESSect-12.2 P-16ESSect-12.2 P-17ESSect-12.2 P-18ESSect-12.2 P-19ESSect-12.2 P-20ESSect-12.2 P-21ESSect-12.2 P-22ESSect-12.2 P-23ESSect-12.2 P-24ESSect-12.2 P-25ESSect-12.2 P-26ESSect-12.2 P-27ESSect-12.2 P-28ESSect-12.2 P-29ESSect-12.2 P-30ESSect-12.2 P-31ESSect-12.2 P-32ESSect-12.2 P-33ESSect-12.2 P-34ESSect-12.2 P-35ESSect-12.2 P-36ESSect-12.2 P-37ESSect-12.2 P-38ESSect-12.2 P-39ESSect-12.2 P-40ESSect-12.2 P-41ESSect-12.2 P-42ESSect-12.2 P-43ESSect-12.2 P-44ESSect-12.2 P-45ESSect-12.2 P-46ESSect-12.2 P-47ESSect-12.2 P-48ESSect-12.2 P-49ESSect-12.2 P-50ESSect-12.2 P-51ESSect-12.2 P-52ESSect-12.2 P-53ESSect-12.2 P-54ESSect-12.3 P-1TYSect-12.3 P-2TYSect-12.3 P-3TYSect-12.3 P-4TYSect-12.3 P-5TYSect-12.3 P-1ESSect-12.3 P-2ESSect-12.3 P-3ESSect-12.3 P-4ESSect-12.3 P-5ESSect-12.3 P-6ESSect-12.3 P-7ESSect-12.3 P-8ESSect-12.3 P-9ESSect-12.3 P-10ESSect-12.3 P-11ESSect-12.3 P-12ESSect-12.3 P-13ESSect-12.3 P-14ESSect-12.3 P-15ESSect-12.3 P-16ESSect-12.3 P-17ESSect-12.3 P-18ES