CS402 ASSIGNMENT 1 SOLUTION 2021. CS402 ASSIGNMENT 1 SOLUTION spring 2021.

# CS403 ASSIGNMENT 1 SOLUTION 2021

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Precis. Re, recursive definition of re, defining languages via re, x*, x+, a+b*, language of strings having exactly one a, language of strings of even period, language of strings of peculiar period, re defines precise language (as remark), language of strings having at the least one a, language of strings having at least one a and one b, language of strings beginning with aa and ending in bb, language of strings beginning with and ending in extraordinary letters.

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### CS402 ASSIGNMENT 1 SOLUTION 2021

Recursive definition of ordinary expression(re). Step 1: each letter of σ inclusive of λ is a regular expression. Also are ordinary expressions. Step three: not anything else is a regular expression. Approach 3 (ordinary expressions) recall the language l=λ, x, xx, xxx,… of strings, defined over σ = x. We can write this language because the kleene star closure of alphabet σ or l=σ* =x* . CS402 ASSIGNMENT 1 SOLUTION 2021

This language also can be expressed by using the normal expression x* similarly the language l=x, xx, xxx,…, described over σ = x, may be expressed through the normal expression x+. Now remember any other language l, which includes all possible strings, described over σ = a, b. This language also can be expressed by using the regular expression (a + b)*. Now don’t forget every other language l, of strings having exactly one a, described over σ = a, b, then it’s regular. CS402 ASSIGNMENT 1 SOLUTION 2021

Expression can be b*ab*. Now remember any other language l, of even duration, described over σ = a, b, then it’s everyday expression may be ((a+b)(a+b))*. Now recall every other language l, of peculiar period, described over σ = a, b, then it’s everyday expression can be (a+b)((a+b)(a+b))* or ((a+b)(a+b))*(a+b). CS402 ASSIGNMENT 1 SOLUTION 2021

Remark it can be mentioned that a language can be expressed by means of multiple everyday expression, whilst given a everyday expression there exist a completely unique language generated by that regular expression.

Instance don’t forget the language, defined over σ = a , b of words having at least one a, may be expressed by way of a ordinary expression (a+b)*a(a+b)*. Recollect the language, described over σ = a, b of words having at least one a and one b, can be expressed by using a everyday expression (a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*. CS402 ASSIGNMENT 1 SOLUTION 2021

Recall the language, defined over σ =a, b, of phrases beginning with double a and finishing in double b then its regular expression can be aa(a+b)*bb recall the language, defined over σ =a, b of words starting with a and finishing in b or beginning with b and ending in a, then its normal expression can be a(a+b)*b+b(a+b)*a.

CS402 ASSIGNMENT 1 SOLUTION 2021