Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. © 1984 Academic Press, Inc.

We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. The open map bisimulation is shown to coincide with the extended bisimulation of Hennessy and Stirling. Finally we formulate Milners operational semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation

The expressiveness of branching time tense (temporal) logics whose eventually operators are relativised to general paths into the future is investigated. These logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions. It is shown that the presence of formulae expressing the future perfect enables one to prove that the expressiveness of the logic can be charaeterised by a notion of bisimulation on the generalised transition systems. The future perfect is obtained by adding a past tense operator to the language. Finally the power of various tense languages from the literature are

This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of di#erent and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency.

We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's anti-foundation axiom and it is constructed along the lines of the anti-founded model for SCCS given by Aczel. We revisit Aczel's semantics for SCCS where we prove a unique fixpoint theorem under the assumption of guarded recursion. Then we consider Milner's extension of SCCS to include a finite delay operator ". Working with fair bisimilarity we construct a fully abstract model, which is also fully abstract for fortification. We discuss the solution of recursive equations in the model. The paper is concluded with an investigation of the algebraic theory of fair bisimilarity. Keywords: fairness, anti-foundation, finite delay, parallelism, fair bisimilarity, fortification. This paper was composed while I was unemployed and an unofficial visitor at the Department of Mathematics, University of Ioannina, Greece. My than...

We generalise Winskel's trees [15] (which underlie the synchronization trees) to allow for fairness constraints to be modelled. We obtain a category of generalized trees, in which semantic operations arise as categorical constructions: sum is a coproduct, while the synchronous and asynchronous parallel composition are restrictions of the product. We investigate a natural partial order on the generalized trees, proposed in Hennessy [8], with respect to which the generalized trees form a dcpo GTr and the above-mentioned operations are continuous, except for the synchronous and asynchronous product. We extend to a category (and dcpo) of generalized synchronization trees L-GTr over a synchronization algebra L. Milner's [11] SCCS with a finite delay operator " is interpreted in SCCS-GTr. The interpretation is consistent with the operational semantics in the sense that for any term P and sequence u of action labels, P admits u if and only if u is the sequence of action labels of some sequenc...

A signature \Sigma gives rise to a language L \Sigma (Var) by extending \Sigma with variables x 2 Var and binding constructs ¯x and x, corresponding to least and greatest fixed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone \Sigma-algebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results provide techniques for relating syntactic and semantic concepts such as in full abstraction or completeness proofs. In the presence of an involutive antitone map on a bicomplete dcpo D we may translate the language L \Sigma (Var) into one with least fixed points only such that meanings are preserved. This allows an approximative semantics where least and greatest fixed points are simultaneously approximated by `unwindings' in the syntax, provided that the limit semantics is substitutive. We discuss the principal difficulties of simultaneous unwindings in the absenc...

Abstract. Although liveness and fairness have been used for a long time in classical model checking, with process-algebraic methods they have seen far less use. One problem is combining fairness with the compositionality of process algebra. In this article we analyse this problem, and then present an approach for using a class of fairness constraints. The approach fulfills all the requirements of compositionality and is compatible with an existing semantics. It is based on the standard LTS model and does not require new fairness-related constructs or rules for the process algebra. Therefore, it avoids potential conflicts between the fairness requirements and the underlying transition system. Although adding fairness can create an infinite subsystem, a larger system in which the subsystem is placed can still be finite. We present an algorithm for constructing a finite LTS which is equivalent to the larger system in every case that an exact finite representation exists, and which otherwise is a conservative estimate of it. However, checking whether an exact finite representation exists is costlier than building the representation, namely, it is PSPACE-complete in the size of an intermediate parameter system. 1

We recast Milner's work on SCCSffl, a calculus for finite but unbounded delay based on SCCS, by giving a denotational semantics for admissibility of infinite computations on a bifinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model in D \Theta K for an operational preorder which generalizes Milner's fortification. Our preorder includes divergence and its restriction to finite behavior corresponds to Abramsky's finitary preorder. By virtue of bifiniteness of D \Theta K we obtain a Stone dual at the level of objects. Since Milner's delay operators ffl and ffi turn out to correspond to the greatest, respectively least, fixed point on K, we consequently enrich SCCS with an additional recursive binding modeled as the greatest fixed point. For the body 1x + p, the new recursive binding imposes finite delay, whereas the ordinary recursion admits infinite, as well as finite, delay of p. We define a notion of admissibility and a denotational semantics...

this paper I propose a much richer final universe for the study of fairness than that used in [Hart1] and [Hart2]. In my view the semantics to finite delay, initiated in [Miln], is too course to make intuitively desirable distinctions, so that something like the present proposal is needed. It should be noted that the idea behind my proposal may already be seen in [Henn1].