Given an NFA, is there a way to determine whether it accepts all strings constructed from its alphabet, without having to iterate over the infinite set of possible strings?
Determining whether a nondeterministic finite automaton accepts every possible string
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Sure! Here's one algorithm:
There may be a faster algorithm than this (step (1) could take time exponential in the size of the input NFA), but this shows that there is indeed some algorithm for solving this problem.