. 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...

This paper describes the Process Algebra Compiler (PAC), a front-end generator for process-algebra-based verification tools. Given descriptions of a process algebra's concrete and abstract syntax and semantics as structural operational rules, the PAC produces syntactic routines and functions for computing the semantics of programs in the algebra. Using this tool greatly simplies the task of adapting verification tools to the analysis of systems described in different languages; it may therefore be used to achieve source-level compatibility between different verication tools. Although the initial verication tools targeted by the PAC are MAUTO and the Concurrency Workbench, the structure of the PAC caters for the support of other tools as well.

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this paper we put forth a process algebraic semantics for statecharts agreeing with [19]. In particular, we provide a translation of statecharts into a process algebra with state refinement , a new operator introduced by the authors in [22]. The semantics of a statechart is then given by the labeled transition system (LTS) of its translation, as defined by the process algebra's structural operational semantics (SOS). The benefits to be reaped by giving statecharts a process algebraic semantics include the following:

We present Persistent Turing Machines (PTMs), a new way of interpreting Turing-machine computation, one that is both interactive and persistent. A PTM repeatedly receives an input token from the environment, computes for a while, and then outputs the result. Moreover, it can \remember" its previous state (work-tape contents) upon commencing a new computation. We show that the class of PTMs is isomorphic to a very general class of eective transition systems, thereby allowing one to view PTMs as transition systems \in disguise." The persistent stream language (PSL) of a PTM is a coinductively dened set of interaction streams : innite sequences of pairs of the form (w i ; w o ), recording, for each interaction with the environment, the input token received by the PTM and the corresponding output token. We dene an innite hierarchy of successively ner equivalences for PTMs over nite interaction-stream prexes and show that the limit of this hierarchy does not coincide with PSL-equivalence. The presence of this \gap" can be attributed to the fact that the transition systems corresponding to PTM computations naturally exhibit unbounded nondeterminism. We also consider amnesic PTMs, where each new computation begins with a blank work tape, and a corresponding notion of equivalence based on amnesic stream languages (ASLs). We show that the class of ASLs is strictly contained in the class of PSLs. Amnesic stream languages are representative of the classical view of Turing-machine computation. One may consequently conclude that, in a stream-based setting, the extension of the Turing-machine model with persistence is a nontrivial one, and provides a formal foundation for reasoning about programming concepts such as objects with static elds. We additional...

Traditionally, in process calculi, relations over open terms, i.e., terms with free process variables, are defined as extensions of closed-term relations: two open terms are related if and only if all their closed instantiations are related. Working in the context of bisimulation, in this paper we study a different approach; we define semantic models for open terms, so-called conditional transition systems, and define bisimulation directly on those models. It turns out that this can be done in at least two different ways, one giving rise to De Simone's formal hypothesis bisimilarity and the other to a variation which we call hypothesis-preserving bisimilarity (denoted t fh and t hp, respectively). For open terms, we have (strict) inclusions t fh /t hp / t ci (the latter denoting the standard ``closed instance' ' extension); for closed terms, the three coincide. Each of these relations is a congruence in the usual sense. We also give an alternative characterisation of t hp in terms of nonconditional transitions, as substitution-closed bisimilarity (denoted t sb). Finally, we study the issue of recursion congruence: we prove that each of the above relations is a congruence with respect to the recursion operator; however, for t ci this result holds under more restrictive conditions than for tfh and thp.]

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Structural Operational Semantics (SOS) is a widely used formalism for specifying the computational meaning of programs, and is commonly used in specifying the semantics of functional languages. Despite this widespread use there has been relatively little work on the imetatheoryj for such semantics. As a consequence the operational approach to reasoning is considered ad hoc since the same basic proof techniques and reasoning tools are reestablished over and over, once for each operational semantics speciøcation. This paper develops some metatheory for a certain class of SOS language speciøcations for functional languages. We deøne a rule format, Globally Deterministic SOS (gdsos), and establish some proof principles for reasoning about equivalence which are sound for all languages which can be expressed in this format. More speciøcally, if the SOS rules for the operators of a language conform to the syntax of the gdsos format, then ffl a syntactic analogy of continuity holds, which rel...

Traditionally, traces are the sequences of labels associated with paths in transition systems X # P(A X).

We introduce the lambda-coiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final F-coalgebra, generalising the basic coiteration schema as given by finality. The duals of primitive recursion and course-of-value iteration, which are known extensions of coiteration, arise as instances of our framework. One can furthermore obtain schemata justifying recursive specifications that involve operators such as addition of power series, regular operators on languages, or parallel and sequential composition of processes. Next...