Multiple choice

Given below are two finite state automata (→ indicates the start state and F indicates a final state)

Y: | | a | b | |-----------------|---|---| | $\rightarrow$ 1 | 1 | 2 | | 2(F) | 2 | 1 |

Z: | | a | b | |-----------------|---|---| | $\rightarrow$ 1 | 2 | 2 | | 2(F) | 1 | 1 |

Which of the following represents the product automaton Z × Y?

  1. | | a | b | |-----------------|---|---| | $\rightarrow$ P | S | R | | Q | R | S | | R(F) | Q | P | | S | Q | P |
  2. || a | b | |-----------------|---|---| | $\rightarrow$ P | S | Q | | Q | R | S | | R(F) | Q | P | | S | P | Q |
  3. | | a | b | |-----------------|---|---| | $\rightarrow$ P | Q | S | | Q | R | S | | R(F) | Q | P | | S | Q | P |
  4. || a | b | |-----------------|---|---| | $\rightarrow$ P | S | Q | | Q | S | R | | R(F) | Q | P | | S | Q | P |
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