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On the power of bounded concurrency I: finite automata
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Journal of Computer and System Sciences
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SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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We present a general result, similar to Rice's theorem, concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency, such as statecharts and abstract parallel automata, which we denote by CFAs (Concurrent Finite Automata). On one extreme, the complexity of detecting non-trivial properties that preserve equivalence of machines, i.e. properties of the accepted language, on finite automata, can be as little as O(1). On the other extreme, Rice's theorem states that all such properties on Turing machines are undecidable. We state that all the non-trivial properties of the regular (or @w-regular) languages, are PSPACE-hard on CFAs with @e-moves and on CFAs without @e-moves accepting infinite words. We also extend this result to CFAs without @e-moves accepting finite words that satisfy a condition that holds for many properties.