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A b s t r a c tWe study the complexity of the problem of converting a deterministic finite automaton (DFA) to a minimum equivalent nondeterministic finite automaton (NFA). More generally, let A ~ B denote the problem of converting a given FA of type A to a minimum FA of type B. We show that many of these optimal-conversion (or minimization) problems are computationally hard. We also study the complexity of decision problems for finite automata and present many fundamental decision problems which are computationally intractable even when the input is a DFA or a NFA with limited nondeterminism (such as unambiguous FA, or DFA's extended with one nondeterministic operation). I n t r o d u c t i o n

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