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Fundamenta Informaticae
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We show inapproximability results concerning minimization of nondeterministic finite automata (nfa's) as well as regular expressions relative to given nfa's, regular expressions or deterministic finite automata (dfa's). We show that it is impossible to efficiently minimize a given nfa or regular expression with n states, transitions, resp. symbols within the factor o(n), unless P = PSPACE. Our inapproximability results for a given dfa with n states are based on cryptographic assumptions and we show that any efficient algorithm will have an approximation factor of at least $\frac{n}{poly({\rm log} n)}$. Our setup also allows us to analyze the minimum consistent dfa problem.