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Design a DFA that accepts all strings contain $bbb$  

regular expression $(a+b)^*bbb(a+b)^*$

then take complement of DFA such that no string has $3$ consecutive occurrences of the letter $b$.

having regular expression $(a+ba+bba)^*(\epsilon + b+ bb)$

edited by
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a*((ba+)+(bba+))*

–3 votes
–3 votes

In this ,firstly make the dfa of the language which accept all strings from the alphabet (a,b) such that all string contain three consecutive occurrence of the letter b ,then make non final state as final state and final state as non final,initial state will remain same then it become the dfa that accept all string not containing three consecutive b's.

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