Construct the moore machine of {a,b} to count the number ofoccurrences of the substring “ab”.

Sure, here is a step-by-step guide to construct a Moore machine to count the number of occurrences of the substring "ab" in a string over {a,b}:

1. Define the states:

   • We need three states:
     • Q0: Initial state, no 'a' or 'ab' has been encountered yet.
     • Q1: 'a' has been encountered, waiting for 'b' to complete 'ab'.
     • Q2: 'ab' has been encountered.

2. Define the output function:

   • For states Q0 and Q1, the output function will be 0 because 'ab' has not been encountered yet.
   • For state Q2, the output function will be 1 because 'ab' has been encountered.

3. Define the state transition function:

   • From Q0, if the input is 'a', the machine goes to Q1. If the input is 'b', the machine stays in Q0.
   • From Q1, if the input is 'a', the machine stays in Q1. If the input is 'b', the machine goes to Q2.
   • From Q2, if the input is 'a', the machine goes to Q1. If the input is 'b', the machine stays in Q2.

4. Draw the Moore machine:

   • Draw three circles representing the three states Q0, Q1, and Q2.
   • Mark Q0 as the initial state