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What is regular expression corresponding to the language of strings of even lengths over the alphabet of {a, b}?
- a)(aa + bb + ba + ab)*
- b)(aa + bb)*
- c)(ab + bb + ba)*
- d)a*b*a*b*
Correct answer is option 'A'. Can you explain this answer?
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What is regular expression corresponding to the language of strings of...
The regular expression corresponding to the language of strings of even lengths over the alphabet of {a, b} is ((a + b)2)* which is equivalent to (aa + bb + ba + ab)*. In choice (b) the string ‘ab’ is not present. In choice (c) the string ‘aa’ is not present. In choice (d) odd length strings are also acceptable.
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What is regular expression corresponding to the language of strings of...
Regular expression for even length strings over {a, b}
Regular expressions are a sequence of characters that form a search pattern. In computer science, regular expressions are used to match patterns in strings. The regular expression corresponding to the language of strings of even lengths over the alphabet of {a, b} is (aa bb ba ab)*.
Explanation:
The regular expression (aa bb ba ab)* matches strings that contain zero or more occurrences of the four strings aa, bb, ba, and ab. Since the language we are interested in is the language of strings of even lengths over {a, b}, the regular expression (aa bb ba ab)* is a good candidate for matching such strings.
Here is why:
- The regular expression matches strings that contain only the characters a and b since these are the only characters in the alphabet.
- The regular expression matches the empty string since it contains zero occurrences of aa, bb, ba, and ab.
- The regular expression matches strings of even lengths since each occurrence of aa, bb, ba, and ab contributes two characters to the string.
For example, here are some strings that are matched by the regular expression:
- "" (the empty string)
- "aa"
- "bb"
- "baab"
- "bbaaabbaba"
None of these strings contain an odd number of characters, so they are all in the language of strings of even lengths over {a, b}.
Conclusion:
The regular expression (aa bb ba ab)* matches strings that are of even lengths over the alphabet of {a, b}.
Regular expressions are a sequence of characters that form a search pattern. In computer science, regular expressions are used to match patterns in strings. The regular expression corresponding to the language of strings of even lengths over the alphabet of {a, b} is (aa bb ba ab)*.
Explanation:
The regular expression (aa bb ba ab)* matches strings that contain zero or more occurrences of the four strings aa, bb, ba, and ab. Since the language we are interested in is the language of strings of even lengths over {a, b}, the regular expression (aa bb ba ab)* is a good candidate for matching such strings.
Here is why:
- The regular expression matches strings that contain only the characters a and b since these are the only characters in the alphabet.
- The regular expression matches the empty string since it contains zero occurrences of aa, bb, ba, and ab.
- The regular expression matches strings of even lengths since each occurrence of aa, bb, ba, and ab contributes two characters to the string.
For example, here are some strings that are matched by the regular expression:
- "" (the empty string)
- "aa"
- "bb"
- "baab"
- "bbaaabbaba"
None of these strings contain an odd number of characters, so they are all in the language of strings of even lengths over {a, b}.
Conclusion:
The regular expression (aa bb ba ab)* matches strings that are of even lengths over the alphabet of {a, b}.
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