# Regular expression for the language of all odd length strings in theory of automata

## Write the Regular expression for the language of all odd length strings defined over ∑ = {a, b}?

Accepted Strings:

These all strings are the part of the language so should be accepted by regular expression.

Example strings = {a, b,  aaa, aba, aabba, aabbb,………}and all other strings that contain odd length strings.

Rejected Strings:

These all strings are not part of the language so should be rejected by regular expression.

Example strings = {aa, bb, ab, ba, aaaa, abba, abbb,……………..} and all other strings that do not contain odd length strings.

R.E = (a+b) (aa+bb+ab+ba)*

 Part 1 Part 2 (a+b) (aa+bb+ab+ba)*

Part 1:

Bounding the machine to read only one odd alphabet so the machine can read only a or b.

Part 2:

Bounding the machine to read many times even length alphabet like a machine can read aa or bb or ab or ba and machine can read it many times by repeating the loop(*).

## DFA for all odd-length strings

Write the Regular expression for the language of all even length strings but starts with a defined over ∑ = {a, b}?

Accepted Strings:

These all strings are the part of the language so should be accepted by regular expression.

Example strings = {aa, ab,  aaab, aaab, aabb, abba, ababab………}and all other strings that are started with a and have even length.

Rejected Strings:

These all strings are not part of the language so should be rejected by regular expression.

Example strings = {a, b,  bb, ba, bab, bab, bba, babb,……………..} and all other strings that do not contain odd length strings.

R.E = (ab + aa) (aa+bb+ab+ba)*

 Part 1 Part 2 (ab + aa) (aa+bb+ab+ba)*

Part 1:

Bounding the machine to read the only even alphabet and starting with a.

Part 2:

Bounding the machine to read many times even length alphabet like a machine can read aa or bb or ab or ba and machine can read it many times by repeating the loop(*).

# Write the Regular expression for the language of all even length strings but ends with aa defined over ∑ = {a, b}?

Accepted Strings:

These all strings are part of the language so should be accepted by regular expression.

Example strings = {aa, baaa,  bbaa, babaaa, …….}and all other strings that end with aa and have even length.

Rejected Strings:

These all strings are not part of the language so should be rejected by regular expression.

Example strings = {a, b, ab, ba, bb,  abb, aba, bab, aab, bbab, abbb,……………..} and all other strings that do not contain even length strings and not end with aa.

R.E = (aa+bb+ab+ba)aa

 Part 1 Part 2 (aa+bb+ab+ba)* aa

Part 1:

Bounding the machine to read many times even length alphabet like the machine can read aa or bb or ab or ba and machine can read it many times by repeating the loop(*).

Part 2:

Bounding the machine to read-only aa at the end.

## List of 100+ Important Regular Expression

By:Prof. Fazal Rehman Shamil
CEO @ T4Tutorials