For two languages A and B, let there be DFAs of k1 and k2 states respectively. Then, A union B has a DFA with at most __ states1 pointk1+k2k1k2k1^k2k1/k2
Question
For two languages A and B, let there be DFAs of k1 and k2 states respectively. Then, A union B has a DFA with at most __ states
- point
- k1 + k2
- k1 k2
- k1^k2
- k1/k2
Solution
The answer is k1 + k2.
Here's why:
A DFA (Deterministic Finite Automaton) for a language A or B has a specific number of states, say k1 and k2 respectively.
When we take the union of two languages A and B, we are essentially combining the two languages into one. This means that the DFA for the union of A and B would need to accommodate for all the states in both A and B.
Therefore, the DFA for A union B would have at most k1 + k2 states. This is because it would need to include all the states from A's DFA and all the states from B's DFA.
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