Given below are two finite state automata (→ indicates the start state and F…
2008
Given below are two finite state automata (→ indicates the start state and F indicates a final state)Which of the following represents the product automaton Z×Y?
- A.
A
- B.
B
- C.
C
- D.
D
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Correct answer: A
The product automaton Z×Y is constructed by taking the Cartesian product of states from Z and Y. The start state is (→, →), which corresponds to the combination of both automata's start states. The final states in the product are those where both components are final: Z has state 2 as final (marked F), and Y has state 1 as non-final. Therefore, the product state (2,1) is not final because Y's component is not final. In option A, the state (2,1) is labeled as R(F), incorrectly marking it as final. This violates the product automaton rules. The correct answer must have (2,1) as a non-final state.
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