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.

ion Rule (KFAR) (Baeten, Bergstra & Klop [3]), expresses a global fairness assumption. It says that when possible a system will escape from any cycle of internal actions. Some form of KFAR is crucial for many protocal verifications with unreliable channels, and for that reason preorders and equivalences that satisfy KFAR are of special interest. Must preorders and divergence sensitive ones cannot satisfy KFAR. In Bergstra, Klop & Olderog [7] it is shown that the combination of KFAR with failure semantics is inconsistent, but they formulate a weaker version of KFAR that is satisfied in failure may-semantics. Still the combination of KFAR \Gamma and the liveness requirement appears to require global testing, and is only satisfied in the semantics between contrasimulation (C) and stability respecting branching bisimulation (BB s ). These requirements would reduce the number of suitable preorders to 18. It is in general a good strategy to do your verifications using the finest preorde...

Concurrent constraint programming [Sar89,SR90] is a sim-ple and powerful model of concurrent computation based on the notions of store-as-constraint and process as information transducer. The store-as-valuation conception of von Neu-mann computing is replaced by the notion that the store is a constraint (a finite representation of a possibly infinite set of valuations) which provides partial information about the possible values that variables can take. Instead of “reading” and “writing ” the values of variables, processes may now ask (check if a constraint is entailed by the store) and tell (augment the store with a new constraint). This is a very general paradigm which subsumes (among others) nonde-terminate data-flow and the (concurrent) (constraint) logic programming languages. This paper develops the basic ideas involved in giving a coherent semantic account of these languages. Our first con-tribution is to give a simple and general formulation of the notion that a constraint system is a system of partial infor-mation (a la the information systems of Scott). Parameter passing and hiding is handled by borrowing ideas from the cylindric algebras of Henkin, Monk and Tarski to introduce diagonal elements and “cylindrification ” operations (which mimic the projection of information induced by existential quantifiers). The se;ond contribution is to introduce the notion of determinate concurrent constraint programming languages. The combinators treated are ask, tell, parallel composition, hiding and recursion. We present a simple model for this language based on the specification-oriented methodology of [OH86]. The crucial insight is to focus on observing the resting points of a process—those stores in which the pro-cess quiesces without producing more information. It turns out that for the determinate language, the set of resting points of a process completely characterizes its behavior on all inputs, since each process can be identified with a closure operator over the underlying constraint system. Very nat-ural definitions of parallel composition, communication and hiding are given. For example, the parallel composition of two agents can be characterized by just the intersection of the sets of constraints associated with them. We also give a complete axiomatization of equality in this model, present

Abstract. In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner’s notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action 7 of CCS this is not the case. Therefore, the notion of branching hisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed KS-terms branching bisimulation congruence can be completely axioma-tized by the single axiom scheme: a.(7.(y + z) + y) = a.(y + z) (where a ranges over all actions) and the usual laws for strong congruence. WC also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is. For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching hisimulation equivalence.

The parallel language CSP [H,1985], an earlier version of which was described in [H,1978], has become a major tool for the analysis of structuring methods and proof systems involving paxal-

this paper various semantics in the linear time -- branching time spectrum are presented in a uniform, model-independent way. Restricted to the class of finitely branching, concrete, sequential processes, only fifteen of them turn out to be different, and most semantics found in the literature that can be defined uniformly in terms of action relations coincide with one of these fifteen. Several testing scenarios, motivating these semantics, are presented, phrased in terms of `button pushing experiments' on generative and reactive machines. Finally twelve of these semantics are applied to a simple language for finite, concrete, sequential, nondeterministic processes, and for each of them a complete axiomatization is provided.

Abstract. We propose a denotational model for real time concurrent systems, based on the failures model for CSP. The fixed point theory is based on the Banach fixed point theorem for complete metric spaces, since the introduction of time as a measure makes all recursive operators naturally contractive. This frees us from many of the constraints imposed by partial orders on the treatment of nondeterminism and divergence. 1

A major reason for studying probabilistic processes is to establish a link between a formal model for describing functional system behaviour and a stochastic process. Compositionality is an essential ingredient for specifying systems. Parallel composition in a probabilistic setting is complicated since it gives rise to non-determinism, for instance due to interleaving of independent autonomous activities. This paper presents a detailed study of the resolution of non-determinism in an asynchronous generative setting. Based on the intuition behind the synchronous probabilistic calculus PCCS we formulate two criteria that an asynchronous parallel composition should fulfill. We provide novel probabilistic variants of parallel composition for CCS and CSP and show that these operators satisfy these general criteria, opposed to most existing proposals. Probabilistic bisimulation is shown to be a congruence for these operators and their expansion is addressed.

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...

This paper combines and extends the material of [GG-a/c/d/e], except for the part in [GG-c] on refinement of transitions in Petri nets and the discussion of TCSP-like parallel composition in [GG-e]. An informal presentation of some basic ingredients of this paper appeared as [GG-b]. Among others, the treatment of action refinement in stable and non-stable event structures is new. The research reported here was supported by Esprit project 432 (METEOR), Esprit Basic Research Action 3148 (DEMON), Sonderforschungsbereich 342 of the TU Munchen, ONR grant N00014-92-J-1974 and the Human Capital and Mobility Cooperation Network EXPRESS (Expressiveness of Languages for Concurrency). Contents