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.

In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear- and branching-time temporal logics.

We prove that bisimulation equivalence is decidable for normed pushdown processes. 1 Introduction In the classical theory of automata the expressive power of pushdown automata is matched by context-free grammars. Both accept the same family of languages, the context-free languages. Concurrency theory requires a more intensional exposition of behaviour (as language equivalence need not be preserved in the presence of communicating abstract machines). Many finer equivalences have been proposed. Bisimulation equivalence, due to Park and Milner, has received much attention. Baeten, Bergstra and Klop proved that bisimulation equivalence is decidable for irredundant context-free grammars (without the empty production) . Within process calculus theory these grammars correspond to normed BPA processes. Their proof relies on isolating a complex periodicity from the transition graphs of these processes. Simpler proofs of the result soon followed which expose algebraic structure. Caucal and Monf...

A process # is regular if it is bisimilar to a process # # with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomial-time algorithm. Moreover, if the tested normed PA process # is regular then the process # # can be e#ectively constructed. It implies decidability of bisimulation equivalence for any pair of processes such that one process of this pair is a normed PA process and the other process has finitely many states.

Recently there has been a spurt of activity in concurrency theory centered on the analysis of infinite-state systems. The following two problems have been intensely investigated: (1) given two infinite-state systems, are they equal with respect to a certain equivalence notion?, and (2) given an infinite-state system and a property expressed in a certain temporal logic, does the system satisfy the property? In his CONCUR '96 paper, Faron Moller surveys some of the key results on the decidability and complexity of (1). The purpose of this paper for CONCUR's satellite INFINITY Workshop is to do the same with (2).

All bisimulation problems for pushdown automata are at least PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACE-hard.

this paper we review results about bisimulation, from both the point of view of automata and from a logical point of view. We also consider how bisimulation has a role in finite model theory, and we offer a new undefinability result.

The branching-time temporal logic EF is a simple, but natural fragment of computation -tree logic (CTL) and the modal -calculus. We study the decidability of the model checking problem for EF and infinite-state systems. We use process rewrite systems (PRS) to describe infinite-state systems and define a hierarchy of subclasses of PRS that includes Petri nets, pushdown processes, Basic Parallel Processes (BPP), context-free processes and PA-Processes. Then we establish the exact limits of the decidability of model checking with EF in this hierarchy. Model checking with EF is undecidable for Petri nets and even for parallel pushdown automata (the pushdown extension of Basic Parallel Processes). On the other hand, model checking with EF is decidable for PAD, a process model that subsumes both PA-processes and pushdown processes. Key words: infinite-state systems, temporal logic, EF, model checking, process algebra, PA-processes, pushdown processes 1 Introduction The branching-time tempora...

It is shown that bisimulation equivalence is decidable for the processes generated by (nondeterministic) pushdown automata where the pushdown behaves like a counter. Also finiteness up to bisimilarity is shown to be decidable for the mentioned processes.

We show an effective construction of (a periodicity description of) the maximal simulation relation for a given one-counter net. Then we demonstrate how to reduce simulation problems over one-counter nets to analogous bisimulation problems over one-counter automata. We use this to demonstrate the decidability of various problems, specifically testing regularity and strong regularity of one-counter nets with respect to simulation equivalence, and testing simulation equivalence between a one-counter net and a deterministic pushdown automaton. Various obvious generalisations of these problems are known to be undecidable. 1