A Distribution Law for CCS and a New Congruence Result for the pi-calculus

We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite pi-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the pi-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.Comment: 20 page

Structural operational semantics for stochastic and weighted transition systems

We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature

Unique Parallel Decomposition for the Pi-calculus

A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus, i.e. processes that perform no infinite executions, satisfy this property modulo strong bisimilarity and weak bisimilarity. Our results are obtained by an application of a general technique for establishing unique parallel decomposition using decomposition orders.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269

On Generative Parallel Composition

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.\ud \ud We would like to thank the reviewers for their constructive criticism and for pointing out the relation between BPTSs and the model of Pnueli and Zuck. We also thank Ed Brinksma and Rom Langerak (both of the University of Twente) for fruitful discussions

Calculi for higher order communicating systems

This thesis develops two Calculi for Higher Order Communicating Systems. Both calculi consider sending and receiving processes to be as fundamental as nondeterminism and parallel composition. The first calculus called CHOCS is an extension of Milner's CCS in the sense that all the constructions of CCS are included or may be derived from more fundamental constructs. Most of the mathematical framework of CCS carries over almost unchanged. The operational semantics of CHOCS is given as a labelled transition system and it is a direct extension of the semantics of CCS with value passing. A set of algebraic laws satisfied by the calculus is presented. These are similar to the CCS laws only introducing obvious extra laws for sending and receiving processes. The power of process passing is underlined by a result showing that the recursion operator is unnecessary in the sense that recursion can be simulated by means of process passing and communication. The CHOCS language is also studied by means of a denotational semantics. A major result is the full abstractness of this semantics with respect to the operational semantics. The denotational semantics is used to provide an easy proof of the simulation of recursion. Introducing processes as first class objects yields a powerful metalanguage. It is shown that it is possible to simulate various reduction strategies of the untyped λ-Calculus in CHOCS. As pointed out by Milner, CCS has its limitations when one wants to describe unboundedly expanding systems, e.g. an unbounded number of procedure invocations in an imperative concurrent programming language P with recursive procedures. CHOCS may neatly describe both call-by-value and call-by-reference parameter mechanisms for P. We also consider call-by-name and lazy parameter mechanisms for P. The second calculus is called Plain CHOCS. Essential to the new calculus is the treatment of restriction as a static binding operator on port names. This calculus is given an operational semantics using labelled transition systems which combines ideas from the applicative transition systems described by Abramsky and the transition systems used for CHOCS. This calculus enjoys algebraic properties which are similar to those of CHOCS only needing obvious extra laws for the static nature of the restriction operator. Processes as first class objects enable description of networks with changing interconnection structure and there is a close connection between the Plain CHOCS calculus and the π-Calculus described by Milner, Parrow and Walker: the two calculi can simulate one another. Recently object oriented programming has grown into a major discipline in computational practice as well as in computer science. From a theoretical point of view object oriented programming presents a challenge to any metalanguage since most object oriented languages have no formal semantics. We show how Plain CHOCS may be used to give a semantics to a prototype object oriented language called 0.Open Acess