Question

Construct the state digraph (including accept states) of a Moore machine that accepts all strings that start with b and end with baa. The input alphabet is A = {a, b].

Answer 1

Please follow the below example to construct state digraph of a Moore machine that accepts all strings that start with b and end with baa:

Let S0 be the starting state. The first thing you need to do is make sure that the first letter is a b, so we'll have the rules:

S0→aS1, S0→bS2

and if the machine is in state S1 it will remain there. If the machine gets to state S2, all we need to do is make it so that the accepting state is reached after any occurrence of the sequence baa, so that if the string ends with such a sequence the machine will be in an accepting state. Thus we want transition rules

S2→bS3, S3→aS4, S4→aS5

with S5 the accepting state. If we run into a letter which is not part of the sequence baa, we want to restart our search for baa, which we do by returning to the state S2. Thus we add the rules

S2→aS2, S3→bS2, S4→bS2, S5→a,bS2