Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes can be said to exhibit the same behaviour, and a plethora of behavioural equivalences exists today. Their main rationale has been to capture behavioural aspects that language or trace equivalences do not take into account. The theory of finite-state systems and their equivalences can now be said to be well-established. There are many automatic verification tools for their analysis which incorporate equivalence checking. Sound and complete equational theories exist for the various known equivalences, an elegant example is [18]. One may be led to wonder what the results will look like for infinite-state systems. Although language equivalence is decidable

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.

Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant context-free grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goal-directed rules. The decision procedure also provides the essential part of the bisimulation relation between two processes which underlies their equivalence. We also show how to obtain a sound and complete sequent-based equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful tableau.

A recent theorem [3, 7, 19] shows that strong bisimilarity is decidable for the class of normed BPA processes, which correspond to a class of context-free grammars generating the ffl-free context-free languages. In [21] Huynh and Tian have shown that readiness and failure equivalence are undecidable for BPA processes. In this paper we examine all other equivalences in the linear/branching time hierarchy [13] and show that none of them are decidable for normed BPA processes. 1 Introduction In the field of process theory much attention has been devoted to the study of process calculi and in particular to behavioural semantics for these calculi. A variety of equiv- Supported by the European Communities under RACE project no. 1046 (SPECS) and ESPRIT Basic Research Action 3006 (CONCUR).This paper was written during a visit of the first author to Edinburgh. y Supported via a position at Aalborg University and by the Danish Research Academy. 2 1 Introduction alences have been propose...

. Recent results show that strong bisimilarity is decidable for the class of Basic Parallel Processes (BPP), which corresponds to the subset of CCS definable using recursion, action prefixing, nondeterminism and the full merge operator. In this paper we examine all other equivalences in the linear/branching time hierarchy [12] and show that none of them are decidable for BPP. 1 Introduction Much attention has been devoted to the study of process calculi and in particular to behavioural semantics for these calculi. In order to capture the behavioural aspects of processes, a variety of equivalences have been proposed. Various criteria exist for comparing the merits and deficiencies of these equivalences. A systematic approach consists of classifying the equivalences according to their coarseness. For this purpose van Glabbeek proposed the linear/branching time spectrum which is illustrated in Figure 1 [12]. The least discriminating equivalences are at the bottom of the diagram. Arrows i...

We present an elementary algorithm for deciding bisimulation equivalence between arbitrary context-free processes. This improves on the state of the art algorithm of Christensen, Huttel and Stirling consisting of two semi-decision procedures running in parallel, which prohibits any complexity estimation. The point of our algorithm is the effective construction of a finite relation characterizing all bisimulation equivalence classes, whose mere existence was exploited for the above mentioned decidability result.

CCS is a universal formalism: any computable function is computed by some CCS agent. Moreover, one can reduce the halting problem for Turing machines to the problem of deciding bisimilarity of two CCS agents, thus demonstrating the undecidability of the equivalence checking problem. In this paper, we demonstrate the limits of decidability of CCS. In particular, we show that by simply disallowing either of communication or both restriction and relabelling, we arrive at a sublanguage which still describes a rich class of infinite state systems but for which bisimulation is decidable. We also demonstrate complete axiomatisations for these sublanguages. We compare these results with the undecidability of all other common equivalences.

this paper we survey recent developments and current trends within a new field of study within process algebra, namely that of decidability issues for processes with infinite transition graphs.

Recently it has been shown that the class of BPA (or context-free) processes can be widely used to describe sequential processes and to define their semantics. This class has been intensively studied. Bisimilarity and regularity appeared to be decidable within the BPA processes (see [CHS95], [BCS96]). We extend these processes with a deadlocking state into BPA ffi systems. We show that the BPA ffi class is more expressive w.r.t. bisimulation equivalence but it remains language equivalent to BPA . We prove that bisimilarity and regularity remain decidable in the BPA ffi class. Finally we give a characterisation of those BPA ffi processes which can be equivalently (up to bisimilarity) described within the `pure' BPA syntax. Keywords: context-free processes, BPA , deadlock, bisimilarity, regularity, language equivalence Chapter 1 Introduction The problem of determining whether a program satisfies a given specification is one of the main issues in theoretical computer science. Tradit...