On deciding trace equivalences for processes

Abstract

In this paper, we investigate the complexity of deciding trace, maximal trace and ω-trace 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. (1) Trace, maximal trace and ω-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 ω-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 Π 2 p -complete while the ω-trace equivalence is NL-complete and the trace equivalence is decidable in polynomial time by a dynamic programming algorithm. 2. (2) Trace, maximal trace and ω-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 ω-trace equivalences are NL-complete.