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On deciding trace equivalences for processes. (English) Zbl 0783.68043
Summary: We investigate the complexity of deciding trace, maximal trace and \(\omega\)-equivalences for finite state processes and recursively defined processes specified by normed context-free grammars (CFGs) in Greibach normal form (GNF). The main results are as follows:
(1) Trace, maximal trace and \(\omega\)-trace equivalences for processes specified by normed GNF CFGs are all undecidable. For this class of processes, the regularity problem with respect to trace, maximal trace or \(\omega\)-trace equivalence is also undecidable. Moreover, all these undecidability results hold even for locally unary processes. For processes specified by unary GNF CFGs, the maximal trace equivalence is \(\prod^ p_ 2\)-complete while the \(\omega\)-trace equivalence is \(NL\)- complete and the trace equivalence is decidable in polynomial time by a dynamic programming algorithm.
(2) Trace, maximal trace and \(\omega\)-trace equivalences for finite state processes are PSPACE-complete. This holds even for locally unary finite state processes. For unary finite state processes, the maximal trace equivalence is co-\(NP\)-complete while trace and \(\omega\)-trace equivalences are \(NL\)-complete.

MSC:
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
68Q55 Semantics in the theory of computing
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