The complexity of readiness and failure equivalences for processes

The authors study the complexity of deciding readiness and failure equivalences for finite state processes and for recursively defined processes specified by normal context-free grammars (CFGs) in Greibach normed form (GNF). The results are as follows: (1) For processes specified by normed GNF CFGs, readiness and failure equivalences are undecidable. In the unary case, they are Π₂^p-complete. The regularity problem for failure or readiness equivalence is undecidable while it is NL-complete for bisimulation equivalence. (2) For finite state processes, readiness and failure equivalences are PSPACE-complete. They are co-NP-complete for unary finite state processes and for acyclic finite state processes, NL -complete for unary acyclic finite state processes and L-complete for finite tree processes. The author´s results provide a complete characterization of the computational complexity of deciding readiness and failure equivalences