Abstraction in real time process algebra

Lecture Notes in Computer Science, 1992

We present an overview and synthesis of existing results about process algebras for the specification and analysis of timed systems. The motivation is double: present an overview of some relevant and representative approaches and suggest a unifying framework for them. After presenting fundamental assumptions about timed systems and the nature of abstract time, we propose a general model for them: transition systems whose labels are either elements of a vocabulary of actions or elements of a time domain. Many properties of this model are studied concerning their impact on description capabilities and on realisability issues. An o.verview of the language features of the process algebras considered is presented, by focusing on constructs used to express time constraints. The presentation is organised as an exercise of building a timed process algebra from a standard process algebra for untimed systems. The overview is completed by a discussion about description capabilities according to semantic and pragmatic criteria.

Theoretical Computer Science, 1985

We present an axiom system ACP, for communicating processes with silent actions ('z-steps'). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's z-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACP, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP~. Finally, termination of rewriting terms according to the ACP~ axioms is proved using the method of recursive path orderings.

Proceedings of The IEEE, 1994

Recently, significant progress has been made in the development of timed process algebras for the specification and analysis of real-time systems. This paper describes a timed process algebra called ACSR, which supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real systems accurately, ACSR supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization. The paper also includes a brief overview of other timed process algebras and discusses similarities and differences between them and ACSR.

Fundamenta Informaticae - FUIN, 2001

Critical issues that arise when process algebras are used for protocol specifications are discussed. To overcome some of these problems, a process algebra for protocol specifications is presented. It is based on Milner's Calculus of Communicating Systems, which is enriched by time and network reasoning. Several bisimulation based semantics for the calculus are defined and their properties are discussed.

Electronic Notes in Theoretical Computer Science, 2006

This paper describes three real-time process algebras, ACSR, PACSR and ACSR-VP. ACSR is a resource-bound real-time process that supports synchronous timed actions and asynchronous instantaneous events as well as the notions of resource, priority, exception, and interrupt. PACSR is a probabilistic extension of ACSR with resources that can fail and associated failure probabilities. ACSR-VP extends ACSR with value passing between processes and parameterized process de nitions. This paper also provides three simple real-time system examples to illustrate the expressive power and analysis technique of each process algebra.

Acta informatica, 2001

Process algebras are a frequently used tool for the speci cation and veri cation of distributed reactive systems. In process algebras, actions are used to denote the basic entities of systems. In general, actions are just abstract names with no particular interpretation. The semantics of a system description, given in form of a process algebra term, is not in uenced by t h e c hoice of names. In this paper, we equip a process algebra with a simple semantics for the actions, given in the form of dependencies. The action dependencies are to beinterpreted in the Mazurkiewicz sense: independent actions should be able to commute, or from a di erent perspective should be unordered, whereas dependent actions are always ordered. In this approach, the operators are used to describe the conceptual behavioural structure of the system and the action dependencies determine the minimal necessary orderings and thereby the additionally possible parallelism within this structure.

2008

Recently, a number of errors have been found in Process Algebra for Hybrid Systems, which is a well-known formalism for specification of hybrid systems. One of the most basic components of Process Algebra for Hybrid Systems is called Basic Process Algebra with standard relative timing (srt) and Non existence (⊥) abbreviated as BPA ⊥ . One of the errors in Process Algebra for Hybrid Systems can be traced down to this most basic component BPA ⊥ , therefore we think that fixing BPA srt ⊥ is essential in rectifying the errors in Process Algebra for Hybrid Systems. Accordingly, in this report we present two proposals for correcting the process algebra BPA ⊥ .

Topology and Its Applications, 2007

A real-time process algebra is presented that features stochastic delays governed by general distributions. In a setting of weak choice, dependent and independent alternative and parallel composition are distinguished. This enables an expansion law for the parallel operator, as well as modular process definitions.

Ieice Transactions, 2009

The algebra of communicating shared resources (ACSR) is a timed process algebra which extends classical process algebras with the notion of a resource. In analyzing ACSR models, the existing techniques such as bisimulation checking and Hennessy-Milner Logic (HML) model checking are very important in theory of ACSR, but they are difficult to use for large complex system models in practice. In this paper, we suggest a framework to verify ACSR models against their requirements described in an expressive timed temporal logic. We demonstrate the usefulness of our approach with a real world case study.

arXiv (Cornell University), 2010

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of Σ algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding seed algebras. We pointed out that the traditional concept of isomorphism of algebra does not apply here, because there is even no one-one correspondence between the elements of two seed algebras. The lack of this one-one correspondence comes from the non-deterministic choice of transitions of a process. We introduce a technique of hidden operations to mask unwanted details of elements of a seed algebra, which only reflect non-determinism or other implicit control mechanism of process transition. Elements of a seed algebra are considered as indistinguishable if they show the same behavior after these unwanted details are masked. Each class of indistinguishable elements is called a non-hidden closure. We proved that bisimulation of two processes is equivalent to isomorphism of non-hidden closures of two seed algebras representing these two processes. We call this kind of isomorphism a deep isomorphism. We get different models of seed algebra by specifying different axiom systems for the same signature. Each model corresponds to a different kind of bisimulation. By proving the relations between these models we also established relations between 10 different bisimulations, which form a acyclic directed graph.