Ready-trace semantics for concrete process algebra with the priority operator

The authors consider a process semantics intermediate between bi-simulation semantics and readiness semantics, called here ready-trace semantics. The advantage of this semantics is that, while retaining the simplicity of readiness semantics, it is still possible to augment this process model with the mechanism of atomic actions with priority (the theta operator). It is shown that in readiness semantics and failure semantics such as extension with theta is impossible. Ready-trace semantics is considered in the simple setting of concrete process algebra, that is: without abstraction (no silent moves), moreover for finite processes only. For such finite processes without silent moves a complete axiomatisation of ready-trace semantics is given via the method of process graph transformation

Congruence from the Operator's Point of View: Compositionality Requirements on Process Semantics

One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus on a number of process operators, and for each of them attempt to find the widest possible class of congruences. To this end, we impose restrictions on sublanguages of Hennessy-Milner logic, so that a semantics whose modal characterization satisfies a given criterion is guaranteed to be a congruence with respect to the operator in question. We investigate action prefix, alternative composition, two restriction operators, and parallel composition.Comment: In Proceedings SOS 2010, arXiv:1008.190

Failure Trace Semantics for a Process Algebra with Time-outs

This paper extends a standard process algebra with a time-out operator, thereby increasing its absolute expressiveness, while remaining within the realm of untimed process algebra, in the sense that the progress of time is not quantified. Trace and failures equivalence fail to be congruences for this operator; their congruence closure is characterised as failure trace equivalence

A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

Modular specification of process algebras

AbstractThis paper proposes a modular approach to the algebraic specification of process algebras. This is done by means of the notion of a module. The simplest modules are building blocks of operators and axioms, each block describing a feature of concurrency in a certain semantical setting. These modules can then be combined by means of a union operator +, an export operator □, allowing to forget some operators in a module, an operator H, changing semantics by taking homomorphic images, and an operator S which takes subalgebras. These operators enable us to combine modules in a subtle way, when the direct combination would be inconsistent.We give a presentation of equational logic, infinitary conditional equational logic — of which we also prove the completeness — and first-order logic and show how the notion of a formal proof of a formula from a theory can be generalized to that of a proof of a formula from a module. This module logic is then applied in process algebra. We show how auxiliary process algebra operators can be hidden when this is needed. Moreover, we demonstrate how new process combinators can be defined in terms of more elementary ones in a clean way. As an illutration of our approach, we specify some FIFO-queues and verify several of their properties