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Behavioural equivalences on finite-state systems are PTIME-hard. (English) Zbl 1109.68052
Summary: The paper shows a LOGSPACE-reduction from the Boolean circuit value problem which demonstrates that any relation subsuming bisimilarity and being subsumed by trace preorder (i.e., language inclusion) is PTIME-hard, even for finite acyclic labelled transition systems. This reproves and substantially extends the result of J. Balcázar, J. Gabarró and M. Sántha [Formal Asp. Comput. 4, 638–648 (1992; Zbl 0758.68033)] for bisimilarity.

MSC:
68Q25 Analysis of algorithms and problem complexity
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
93A30 Mathematical modelling of systems (MSC2010)
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