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1 . Give DFA's accepting the following languages over the alphabet f 0 ; 1 g: ( a ) ( 1 5 marks ) The

1. Give DFA's accepting the following languages over the alphabet f0; 1g:
(a)(15 marks) The set of all strings with 101 as a substring. Prove the correctness of your DFA using state invariants.
(b)(15 marks) The set of all strings with the 11 as a substring. Prove that your DFA has minimal number of states using techniques shown in class.
(c)(5 marks) The set of strings ending in 110.(no proofs required here)

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