Theory of Automata

Examples of Infinite Regular Expressions



Infinite Regular expressions are used to represent the infinite regular languages. So, the length of infinite regular expressions is always Unlimited.

Example 01

Write the regular expression for the language which accepting all the strings which having all combinations of a’s over ∑ = {a}.

Solution

Language for given example is given below

L = { ε, a, aa, aaa, aaaa, aaaaa, ……….. }

Regular expression for above language is given below

L(R) = a*

Example 02

Write the regular expression for the language which accepting all the strings which having all combinations of a’s except the null string over ∑ = {a}.



Solution

Language for given example is given below

L = {a, aa, aaa, aaaa, aaaaa, ……….. }

Regular expression for above language is given below

L(R) = a+

Example 03

Write the regular expression for the language which accepting all the strings, which having any number of a’s and b’s over ∑ = {a, b}.

Solution

Language for given example is given below

L = {a, b, ab, ba, aab, aba, aaba ……….. }

Regular expression for above language is given below

L(R) = (a+b)*

Example 04

Write the regular expression for the language which accepting all the strings, having only one “b” and any numbers of “a” over ∑ = {a, b}.



Solution

Language for given example is given below

L = {b, ab, aba, abaa, abaaaa, aaaaabaaaaaaa……….. } // all strings having only one “b”

Regular expression for above language is given below

L(R) = a*ba*

Example 05

Write the regular expression for the language which accepting all the strings, which are starting with 1 and ending with 0, over ∑ = {0, 1}.

Solution

Language for given example is given below

L = {10, 100, 11010, 1110, 1111000, ……….. } // starting with 1 and ending with 0

Regular expression for above language is given below

L(R) = 1(0+1)*0

Example 06

Write the regular expression for the language which accepting all the strings having even length, over ∑ = {0}.

Solution

Language for given example is given below

L = { ε, 00, 0000, 000000, 00000000, ……….. }

Regular expression for above language is given below

L(R) = (00)*

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