Standard Process Algebras Research Articles

Modelling mutual exclusion in a process algebra with time-outs

I show that in a standard process algebra extended with time-outs one can correctly model mutual exclusion in such a way that starvation-freedom holds without assuming fairness or justness, even when one makes the problem more challenging by assuming memory accesses to be atomic. This can be achieved only when dropping the requirement of speed independence.

Reactive bisimulation semantics for a process algebra with timeouts

This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with timeout transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra with recursion, and a complete axiomatisation.

A process algebra with global variables

In standard process algebra, parallel components do not share a common state and communicate through synchronisation. The advantage of this type of communication is that it facilitates compositional reasoning. For modelling and analysing systems in which parallel components operate on shared memory, however, the communication-through-synchronisation paradigm is sometimes less convenient. In this paper we study a process algebra with a notion of global variable. We also propose an extension of Hennessy-Milner logic with predicates to test and set the values of the global variables, and prove correspondence results between validity of formulas in the extended logic and stateless bisimilarity and between validity of formulas in the extended logic without the set operator and state-based bisimilarity. We shall also present a translation from the process algebra with global variables to a fragment of mCRL2 that preserves the validity of formulas in the extended Hennessy-Milner logic.

Ensuring liveness properties of distributed systems: Open problems

Often fairness assumptions need to be made in order to establish liveness properties of distributed systems, but in many situations they lead to false conclusions.This document presents a research agenda aiming at laying the foundations of a theory of concurrency that is equipped to ensure liveness properties of distributed systems without making fairness assumptions. This theory will encompass process algebra, temporal logic and semantic models. The agenda also includes the development of a methodology and tools that allow successful application of this theory to the specification, analysis and verification of realistic distributed systems.Contemporary process algebras and temporal logics fail to make distinctions between systems of which one has a crucial liveness property and the other does not, at least when assuming justness, a strong progress property, but not assuming fairness. Setting up an alternative framework involves giving up on identifying strongly bisimilar systems, inventing new induction principles, developing new axiomatic bases for process algebras and new congruence formats for operational semantics, and creating matching treatments of time and probability.Even simple systems like fair schedulers or mutual exclusion protocols cannot be accurately specified in standard process algebras (or Petri nets) in the absence of fairness assumptions. Hence the work involves the study of adequate language or model extensions, and their expressive power.

Compositional bisimulation metric reasoning with Probabilistic Process Calculi

We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of non-expansiveness) captures the essential nature of compositional reasoning and allows now also to reason compositionally about recursive processes. We characterize the distance between probabilistic processes composed by standard process algebra operators. Combining these results, we demonstrate how compositional reasoning about systems specified by continuous process algebra operators allows for metric assume-guarantee like performance validation.

Unguardedness mostly means many solutions

A widely accepted method to specify (possibly infinite) behaviour is to define it as the solution, in some process algebra, of a recursive specification, i.e., a system of recursive equations over the fundamental operations of the process algebra. The method only works if the recursive specification has a unique solution in the process algebra; it is well-known that guardedness is a sufficient requirement on a recursive specification to guarantee a unique solution in any of the standard process algebras. In this paper we investigate to what extent guardedness is also a necessary requirement to ensure unique solutions. We prove a theorem to the effect that all unguarded recursive specifications over BPA have infinitely many solutions in the standard models for BPA . In contrast, we observe that there exist recursive specifications over PA , necessarily involving parallel composition, that have a unique solution, or finitely many solutions in the standard models for PA .

Process algebraic support for web service composition

Web services technology provides a platform on which we can develop distributed services. The interoperability among these services is achieved by various standard protocols. In recent years, several researches suggested that process algebras provide a satisfactory assistance to the whole process of web services development. Business transactions, on the other hand, involve the coordination and interaction between multiple partners. With the emergence of web services, business transactions are conducted using these services. The coordination among the business processes is crucial, so is the handling of faults that can arise at any stage of a transaction. Compensation is an error recovery mechanism to handle faults in business transactions. Compensating CSP (cCSP) is a language defined to model business transactions within the framework of standard CSP process algebra. The language defines a transaction as a process and has the constructs for orchestration of compensations. In this short note, we report a case study showing how cCSP can be used to model business transactions. We also show a mechanical verification technique to verify theoretical properties of the language

CCS with priority guards

It has long been recognised that standard process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority. Various solutions have been proposed. We introduce a new approach, involving the addition of “priority guards” to Milner’s process calculus CCS. In our approach, priority is unstratified, meaning that actions are not assigned fixed levels, so that the same action can have different priority depending where it appears in a program. Unlike in other unstratified accounts of priority in CCS (such as that of Camilleri and Winskel), we treat inputs and outputs symmetrically. We introduce the new calculus, give examples, develop its theory (including bisimulation and equational laws), and compare it with existing approaches. We use leader election problems to show that priority adds expressiveness to both CCS and the π-calculus.

A coalgebraic approach to the semantics of the ambient calculus

Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is—in contrast to the situation in standard process algebra—up to now no satisfying coalgebraic representation of a mobile process calculus. Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems. Crucial features of our modelling are a set of GSOS style transition rules for the ambient calculus, a hardwiring of the so-called hardening relation in the functorial signature, and a set-based treatment of hidden name sharing. The formal representation of this framework is cast in the algebraic–coalgebraic specification language C OC ASL.

Well-behaved flow event structures for parallel composition and action refinement

Flow event structures were introduced as a model for giving semantics to process algebras. However, it turned out that certain restrictions have to be made to make them suitable for this purpose. In this paper, we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators, and for action refinement as a means of regarding processes on different levels of abstraction. First, suitable subclasses are characterised. Then two specific subclasses are proposed. The larger class generalises the one from Castellani and Zhang (Theoret. Comput. Sci. 179 (1997) 203–215), which is not suitable for action refinement. The smaller one is still sufficiently expressive for dealing with all standard process algebras and action refinement.

Embedding untimed into timed process algebra: the case for explicit termination

In ACP-style process algebra the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, different forms of termination can be distinguished: some-time termination, termination before the next clock tick, urgent termination, having terminated. In a setting with the silent action for successful termination (skip). We can recover standard ACP-style process algebras as subtheories of the new theory. The new approach has definite advantages over the standard approach. The paper contributes to ongoing work on relationships between algebras with different timing features.

Embedding Untimed into Timed Process Algebra; the Case for Explicit Termination

In ACP-style process algebra, the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, different forms of termination can be distinguished: some-time termination, termination before the next clock tick, urgent termination, being terminated. In a setting with the silent action τ, we also have silent termination.This leads to problems with the interpretation of atomic actions in timed theories that involve some form of the empty process or some form of the silent action.Reflection on these problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators. Sequential composition remains a basic operator, and thus we have two basic constants for termination, δ for unsuccessful termination (deadlock) and ∊ for successful termination (skip). We can recover standard process algebras as subtheories of the new theory. The new approach has definite advantages over the standard approach.

Discrete time generative–reactive probabilistic processes with different advancing speeds

We present a process algebra expressing probabilistic external/internal choices, multi-way synchronizations, and processes with different advancing speeds in the context of discrete time, i.e. where time is not continuous but is represented by a sequence of discrete steps as in discrete time Markov chains (DTMCs). To this end, we introduce a variant of CSP that employs a probabilistic asynchronous parallel operator whose synchronization mechanism is based on a mixture of the classical generative and reactive models of probability. In particular, differently from existing discrete time process algebras, where parallel processes are executed in synchronous locksteps, the parallel operator that we adopt allows processes with different probabilistic advancing speeds (mean number of actions executed per time unit) to be modeled. Moreover, our generative–reactive synchronization mechanism makes it possible to always derive DTMCs in the case of fully specified systems. We then present a sound and complete axiomatization of probabilistic bisimulation over finite processes of our calculus, that is a smooth extension of the axiom system for a standard process algebra, thus solving the open problem of cleanly axiomatizing action restriction in the generative model. As a further result, we show that, when evaluating steady state based performance measures which are expressible by attaching rewards to actions, our approach provides an exact solution even if the advancing speeds are considered not to be probabilistic, without incurring the state space explosion problem that arises with standard synchronous approaches. We finally present a case study on multi-path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications.

The Box Algebra=Petri Nets+Process Expressions

The paper describes a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics: one based on Petri nets, the other on SOS rules. This consistency can also be extended to a partial order semantics.

The Box Algebra=Petri Nets+Process Expressions

The paper describes a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics: one based on Petri nets, the other on SOS rules. This consistency can also be extended to a partial order semantics.

Recursion and Petri nets

This paper shows how to define Petri nets through recursive equations. It specifically addresses this problem within the context of the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The paper presents a detailed investigation of the solvability of recursive equations on nets in what is arguably the most general setting. For it allows an infinite number of possibly unguarded equations, each equation possibly involving infinitely many recursion variables. The main result is that by using a suitable partially ordered domain of nets, it is always possible to solve a system of equations by constructing the limit of a chain of successive approximations.

A Process Algebra for Timed Systems

A standard process algebra is extended by a new action σ which is meant to denote idling until the next clock cycle. A semantic theory based on testing is developed for the new language. This is characterised in terms of barbs, a variety of ready traces and also characterised as the initial theory generated by a set of equations.

The Algebra of Timed Processes, ATP: Theory and Application

The algebra of timed processes, ATP , uses a notion of discrete global time and suggests a conceptual framework for introducing time by extending untimed languages. The action vocabularly of ATP contains a special element representing the progress of time. The algebra has, apart from standard operators of process algebras such as prefixing by an action, alternative choice, and parallel composition, a primitive unit-delay operator. For two arguments, processes P and Q , this operator gives a process which behaves as P before the execution of a time event and behaves as Q afterwards. It is shown that several d -unit delay constructs such as timeouts and watchdogs can be expressed in terms of the unit-delay operator and standard process algebra operators. A sound and complete axiomatization for bisimulation semantics is studied and two examples illustrating the adequacy of the language for the description of timed systems are given. Finally we provide a comparison with existing timed process algebras.