Process rewrite systems

Many formal models for infinite-state concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and define a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The most general and most expressive class of systems in this hierarchy is called process rewrite systems (PRS). They subsume Petri nets, PA-processes, and pushdown processes and are strictly more expressive than any of these. Intuitively, PRS can be seen as an extension of Petri nets by subroutines that can return a value to their caller. We show that the reachability problem is decidable for PRS. It is even decidable if there is a reachable state that satisfies certain properties that can be encoded in a simple logic. Thus, PRS are more expressive than Petri nets, but not Turing-powerful.

[1]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[2]  Søren Christensen.  Decidability and decomposition in process algebras , 1993 .

[3]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[4]  Nicolas Halbwachs,et al.  Automatic discovery of linear restraints among variables of a program , 1978, POPL.

[5]  Javier Esparza,et al.  On the Model Checking Problem for Branching Time Logics and Basic Parallel Processes , 1995, CAV.

[6]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[7]  Richard Mayr.  Process rewrite systems , 1997, EXPRESS.

[8]  Javier Esparza,et al.  Checking System Properties via Integer Programming , 1996, ESOP.

[9]  Antonín Kucera,et al.  Regularity is Decidable for Normed PA Processes in Polynomial Time , 1996, FSTTCS.

[10]  Richard Mayr.  Combining Petri Nets and PA-Processes , 1997, TACS.

[11]  Jan A. Bergstra,et al.  Algebra of Communicating Processes with Abstraction , 1985, Theor. Comput. Sci..

[12]  Faron Moller,et al.  Infinite Results , 1996, CONCUR.

[13]  Javier Esparza,et al.  Decidability of model checking for infinite-state concurrent systems , 1997, Acta Informatica.

[14]  Javier Esparza,et al.  More infinite results , 2001, INFINITY.

[15]  Ahmed Bouajjani,et al.  Constrained Properties, Semilinear Systems, and Petri Nets , 1996, CONCUR.

[16]  Bernhard Steffen,et al.  Bisimulation Collapse and the Process Taxonomy , 1996, CONCUR.

[17]  Simon L. Peyton Jones,et al.  Imperative functional programming , 1993, POPL '93.

[18]  J. Esparza.  More Innnite Results , 1996 .

[19]  Richard Mayr.  Decidability and complexity of model checking problems for infinite state systems , 1998 .

[20]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[21]  Petr Jancar,et al.  Decidability of a Temporal Logic Problem for Petri Nets , 1990, Theor. Comput. Sci..

[22]  Javier Esparza,et al.  Reachability Analysis of Pushdown Automata: Application to Model-Checking , 1997, CONCUR.

[23]  Richard Mayr.  Model Checking PA-Processes , 1997, CONCUR.

[24]  Didier Caucal,et al.  On the Regular Structure of Prefix Rewriting , 1990, Theor. Comput. Sci..

[25]  L. Dickson.  Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors , 1913 .