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Finite-automaton aperiodicity is PSPACE-complete. (English) Zbl 0733.68038
The following three algorithmical problems are investigated. Given a minimum-state deterministic finite automaton M, is the language L(M)
1) a star-free language (a language expressible through regular expressions without *-operation)? 2) a dot-depth language? 3) a piecewise testable language? It is shown that Problem 1 is PSPACE-complete, and Problems 2 and 3 are logspace complete for NLOG. This solves the open problem from J. Stern [Inf. Control 66, 163-176 (1985; Zbl 0603.68059)], where a polynomial space algorithm for Problem 1 and polynomial time algorithms for Problems 2 and 3 are presented.

MSC:
68Q25 Analysis of algorithms and problem complexity
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
68Q45 Formal languages and automata
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References:
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