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the minimal finite automata accepting the set of all strings over { 0, 1} starting with 1 that interpreted as the binary representation of an integer are congruent to 0 modulo 5 has  ______ states.
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It must be 7 states.

A minimal DFA which accepts strings divisible by 5 contains 5 states.

In the first production you have to add a dead state for transition on 0 and the first state would have transition 1 going to the next state and the rest is as usual for 0mod5.

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