Technische Universit  at M  U N C H E N Institut F  Ur Informatik Simulation Preorder on Simple Process Algebras Simulation Preorder on Simple Process Algebras

We consider the problem of simulation preorder/equivalence between in nitestate processes and nite-state ones. We prove that simulation preorder (in both directions) and simulation equivalence are intractable between all major classes of in nite-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 co-NP-hard; consequently, simulation equivalence between BPA (or BPP) and nite-state processes is also co-NP-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 deterministic 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. Supported by a Research Fellowship granted by the Alexander von Humboldt Foundation and by a Post-Doc grant GA CR No. 201/98/P046.