Question: In this exercise the alphabet ={ a , b }. (1p) Define a DFA A over such that L ( A )={ w * |

In this exercise the alphabet ={a,b}.

  1. (1p) Define a DFA A over such that L(A)={w* | u,v*. w=ubbav} (i.e. the DFA should accept exactly those strings that do not contain substrings of the form bba).

  2. (1p) Define a DFA B over that accepts exactly those strings that have an even number of occurrences of a.

  3. (2p) Construct AB, i.e. use the product construction to build an automaton that accepts the language L(A)L(B).

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