Which regular grammar generates the language consisting of strings containing "aba" or "abb"? Options : S -> a | b | aS | bS S -> abS | abbS | ε S -> abaS | abbS | ε none
Question
Which regular grammar generates the language consisting of strings containing "aba" or "abb"?
Options : S -> a | b | aS | bS S -> abS | abbS | ε S -> abaS | abbS | ε none
Solution
The correct option is "S -> abaS | abbS | ε". This regular grammar generates the language consisting of strings containing "aba" or "abb". Here's why:
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"S -> abaS" means that the grammar can generate strings that contain "aba". After generating "aba", it can generate more strings by replacing the symbol S.
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"S -> abbS" means that the grammar can generate strings that contain "abb". After generating "abb", it can generate more strings by replacing the symbol S.
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"S -> ε" means that the grammar can generate an empty string. This is necessary because "aba" and "abb" are part of the language, and we need to be able to stop generating strings at some point.
The other options are incorrect because they do not generate the language consisting of strings containing "aba" or "abb". For example, "S -> a | b | aS | bS" can generate any string of a's and b's, not just those containing "aba" or "abb". Similarly, "S -> abS | abbS | ε" can generate strings containing "ab" or "abb", but not "aba".
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