Extended Process Rewrite Systems: Expressiveness and Reachability

Abstract

Abstract. We unify a view on three extensions of Process Rewrite Systems (PRS) and compare their expressive power with that of PRS. We show that the class of Petri nets is less expressive up to bisimulation equivalence than the class of PA processes extended with a finite state control unit. Further we show our main result that the reachability problem for PRS extended with a so called weak finite state unit is decidable.

Roadmap of Infinite Results

“…An (α, β)-sePRS ∆ is called a weakly extended (α, β)-process rewrite system ((α, β)-wPRS) iff there is a partial ordering ≤ on Q such that all rewrite rules pE a −→ qF from ∆ satisfy that q ≤ p. The main result (valid for all the classes from the wPRS hierarchy) is that the reachability problem is decidable [30]. The technique from [30] was later extended in [29], where the authors prove the decidability of the problem "given a formula of Hennessy-Milner logic, is there a reachable state satisfying the formula?".…”

On Decidability of LTL Model Checking for Process Rewrite Systems

“…This hierarchy is strict, with a potential exception concerning the classes wPRS and PRS, where the strictness is just our conjecture. For details see [KŘS04b,KŘS04a].…”

“…This control unit enriches PRS by abilities to model a bounded number of arbitrary communication events and global variables whose values are changed only a bounded number of times during any computation. We have proved that the reachability problem remains decidable for wPRS [KŘS04a] and that the problem called reachability Hennessy-Milner 2. We show that model checking (of both finite and infinite runs) of wPRS against negated formulae of A is decidable.…”

“…We show that model checking (of both finite and infinite runs) of wPRS against negated formulae of A is decidable. The proof employs our results presented in [Boz05,KŘS04a,KŘS05] to reduce the problem to LTL model checking for PDA and PN. Thus we get decidability of model checking for wPRS against LTL…”

Monotonic Set-Extended Prefix Rewriting and Verification of Recursive Ping-Pong Protocols

“…MSP rules enrich prefix rewrite rules with the update of the control state. Control states are partially ordered, and a state update can only lead to states that are greater or equal than the current one, like for instance in weak Büchi automata [17,14], or weak Process Rewrite Systems (wPRSs) [16]. Furthermore, when a rule is applied to a word w in the current store T with the result w , both w and w are included in the new store.…”