Technische Universit at M U N C H E N Institut F Ur Informatik Simulation Preorder on Simple Process Algebras 1999 Sfb 342 Methoden Und Werkzeuge F Ur Die Nutzung Paralleler Architekturen Simulation Preorder on Simple Process Algebras

We consider the problem of simulation preorder/equivalence between innnite-state processes and nite-state ones. We prove that simulation preorder (in both directions) and simulation equivalence are intractable between all major classes of innnite-state systems and nite-state ones. This result is obtained by showing that the problem whether a BPA (or BPP) process simulates a nite-state one is PSPACE-hard, and the other direction is coN P-hard; consequently, simulation equivalence between BPA (or BPP) and nite-state processes is also coN P-hard. The decidability border for the mentioned problem is also established. Simulation preorder (in both directions) and simulation equivalence are shown to be decidable in EXPTIME between pushdown processes and nite-state ones. On the other hand, simulation preorder is undecidable between PA and nite-state processes in both directions. The obtained results also hold for those PA and nite-state processes which are deter-ministic and normed, and thus immediately extend to trace preorder. Regularity ((niteness) w.r.t. simulation and trace equivalence is also shown to be undecidable for PA. Finally, we describe a way how to utilize decidability of bisimulation problems to solve certain instances of undecidable simulation problems. We apply this method to BPP processes.