how many DFA can be designed, with a fixed initial state, over an alphabet ∑ =…
how many DFA can be designed, with a fixed initial state, over an alphabet ∑ = {a, b}, and the number of states be two.
Answer: 64 — To determine the number of DFAs with two states and a fixed initial state over alphabet {a, b}, consider the following: Transition Function: Each of the two…
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Correct answer: 64
To determine the number of DFAs with two states and a fixed initial state over alphabet {a, b}, consider the following:
Transition Function: Each of the two states must have transitions for both 'a' and 'b'. This gives 2 × 2 = 4 transition entries. Each entry can go to either of the two states, so there are 2^4 = 16 possible transition functions.
Accepting States: Each of the two states can be accepting or non-accepting. This gives 2^2 = 4 possible combinations of accepting states.
Total DFAs: Multiply the number of transition functions by the number of accepting state combinations: 16 × 4 = 64.
Thus, 64 distinct DFAs can be designed with the given constraints.