Construct the moore machine of {a,b} to count the number ofoccurrences of the substring “ab”.
Question
Construct the moore machine of {a,b} to count the number ofoccurrences of the substring “ab”.
Solution
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}:
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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.
- We need three states:
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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.
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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.
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Draw the Moore machine:
- Draw three circles representing the three states Q0, Q1, and Q2.
- Mark Q0 as the initial state
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