# Regular Expression for an odd number of 0’s or an odd number of 1’s in the strings

## Regular Expression for an odd number of 0’s or an odd number of 1’s in the strings.

Regular Expression : 1*(01*01*)*01* + 0*(10*10*)*10*

## DFA of odd number of 0’s or an odd number of 1’s in the strings

Language of all those strings having an odd number of 0’s or odd number of 1’s.

Reject able strings (not part of the language)

These strings must be rejected by our Regular expression.

• 3 strings of length 1 = {no string}
• 3 strings of length 2 = {00, 11, no more string}
• 3 strings of length 3 = {no string}
• 3 strings of length 4 = {0000, 1111, 1010,…….. and many more similar possible  strings }
• 3 strings of length 7 = {no string}
• 3 strings of length 10 = {0000001111, 1111111100, 0000000000, and many more similar possible  strings }
• 3 strings of length 15 = {no string}
• 3 strings of length 20 = {00000111110000011111, 11111111110000000000, 1010101010, and many more similar possible  strings }
• 3 strings of length 25 = {no string}
• Many more similar possible

Acceptable strings (part of the language)

These strings must be accepted by our Regular expression.

• 3 strings of length 1 = {0, 1, no more string}
• 3 strings of length 2 = {10, 01, no more string}
• 3 strings of length 3 = {000,111,001, ….and many more similar possible  strings }
• 3 strings of length 4 = {0001, 1000, 0111, …and many more similar possible  strings }
• 3 strings of length 7 = {0000000, 1010101, 0000111, …and many more similar possible  strings }
• 3 strings of length 10 = {0000011111, 1010101010, 1111111000, …… and many more similar possible  strings}
• 3 strings of length 15 = {000001111100000, 000001111111111, 111111111111100, …… and many more similar possible  strings }
• 3 strings of length 20 = {00000111111111111111, 00000000000111111111, 00000011111100001110, ….. and many more similar possible  strings }
• 3 strings of length 25 = {0000000000000000000011111, 0000011111000001111100000, 1111111111111110000000000, …….. and many more similar possible  strings }
• Many more similar possible

# Regular Expression : b*(ab*ab*)*ab* + a*(ba*ba*)*ba*

Language of all those strings having an odd number of a’s or odd number of b’s

Reject able strings (not part of the language)

These strings must be rejected by our Regular expression.

• 3 strings of length 1 = {no string}
• 3 strings of length 2 = {aa, bb, no more string}
• 3 strings of length 3 = {no string}
• 3 strings of length 4 = {aaaa, bbbb, baba,…….. and many more similar possible  strings }
• 3 strings of length 7 = {no string}
• 3 strings of length 10 = {aaaaaabbbb, bbbbbbbbaa, aaaaaaaaaa, and many more similar possible  strings }
• 3 strings of length 15 = {no string}
• 3 strings of length 20 = {aaaaabbbbbaaaaabbbbb, bbbbbbbbbbaaaaaaaaaa, bababababa, and many more similar possible  strings }
• 3 strings of length 25 = {no string}
• Many more similar possible

Acceptable strings (part of the language)

These strings must be accepted by our Regular expression.

• 3 strings of length 1 = {a, b, no more string}
• 3 strings of length 2 = {ba, ab, no more string}
• 3 strings of length 3 = {aaa,bbb,aab, ….and many more similar possible  strings }
• 3 strings of length 4 = {aaab, baaa, abbb, …and many more similar possible  strings }
• 3 strings of length 7 = {aaaaaaa, bababab, aaaabbb, …and many more similar possible  strings }
• 3 strings of length 10 = {aaaaabbbbb, bababababa, bbbbbbbaaa, …… and many more similar possible  strings}
• 3 strings of length 15 = {aaaaabbbbbaaaaa, aaaaabbbbbbbbbb, bbbbbbbbbbbbbaa, …… and many more similar possible  strings }
• 3 strings of length 20 = {aaaaabbbbbbbbbbbbbbb, aaaaaaaaaaabbbbbbbbb, aaaaaabbbbbbaaaabbba, ….. and many more similar possible  strings }
• 3 strings of length 25 = {aaaaaaaaaaaaaaaaaaaabbbbb, aaaaabbbbbaaaaabbbbbaaaaa, bbbbbbbbbbbbbbbaaaaaaaaaa, …….. and many more similar possible  strings }
• Many more similar possible

Regular Expression for an odd number of 0 or an odd number of 1 in the strings

## Tutorial: Regular Expression

A detailed tutorial of the regular expression is here in the link of regular expression tutorial. This page contains the practice questions of regular expressions with solutions.

Tutorial covering the topics

• Give a regular expression.
• Describe the strings of the regular expression.
• write a regular expression.
• create all strings from regular expression.
• Generate all strings from regular expression.
• Extract all strings from regular expression.
• Find all strings from regular expression.
• Examples of regular expression.
Prof.Fazal Rehman Shamil (Available for Professional Discussions)
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