Real-time Process Algebra Research Articles

Using Process Algebra to Describe Human and Software Behaviors

Although there are various ways to express actions and behaviors in natural languages, it is found in cognitive informatics that human and system behaviors may be classified into three basic categories: to be, to have, and to do. All mathematical means and forms, in general, are an abstract description of these three categories of system behaviors and their common rules. Taking this view, mathematical logic may be perceived as the abstract means for describing ‘to be,’ set theory for describing 'to have,' and algebras, particularly the process algebra, for describing ‘to do.’ This is a fundamental view toward the formal description and modeling of human and system behaviors in general, and software behaviors in particular, because a software system can be perceived as a virtual agent of human beings, and it is created to do something repeatable, to extend human capability, reachability, and/or memory capacity. The author found that both human and software behaviors can be described by a three-dimensional representative model comprising action, time, and space. For software system behaviors, the three dimensions are known as mathematical operations, event/process timing, and memory manipulation. This paper introduces the real-time process algebra (RTPA) that serves as an expressive notation system for describing thoughts and notions of dynamic software behaviors. Experimental case studies on applications of RTPA in describing the equivalent software and human behaviors as a series of actions and cognitive processes are demonstrated with real-world examples.

Refinement of Actions in a Real-Time Process Algebra with a True Concurrency Model

In this paper, we develop techniques of action refinement in a real-time process algebra that allows urgent interactions to model timeout. Semantic counterpart is carried out in a real-time non-interleaving causality based setting, timed bundle event structures. We show that our refinement notions have the following nice properties: the observable behaviour of the refined system can be inferred compositionally from the observable behaviour of the original system and from the observable behaviour of the processes substituted for the actions; the timed extensions of observational pomset trace equivalence and observational history preserving bisimulation equivalence are both congruences under our refinement; and the syntactic and semantic refinements coincide up to the aforementioned equivalence relations with respect to a cpo-based denotational semantics.

The Real-Time Process Algebra (RTPA)

The real-time process algebra (RTPA) is a set of new mathematical notations for formally describing system architectures, and static and dynamic behaviors. It is recognized that the specification of software behaviors is a three-dimensional problem known as: (i) mathematical operations, (ii) event/process timing, and (iii) memory manipulations. Conventional formal methods in software engineering were designed to describe the 1-D (type (i)) or 2-D (types (i) and (iii)) static behaviors of software systems via logic, set and type theories. However, they are inadequate to address the 3-D problems in real-time systems. A new notation system that is capable to describe and specify the 3-D real-time behaviors, the i>real-time process algebra (RTPA), is developed in this paper to meet the fundamental requirements in software engineering. RTPA is designed as a coherent software engineering notation system and a formal engineering method for addressing the 3-D problems in software system specification, refinement, and implementation, particularly for real-time and embedded systems. In this paper, the RTPA meta-processes, algebraic relations, system architectural notations, and a set of fundamental primary and abstract data types are described. On the basis of the RTPA notations, a system specification method and a refinement scheme of RTPA are developed. Then, a case study on a telephone switching system is provided, which demonstrates the expressive power of RTPA on formal specification of both software system architectures and behaviors. RTPA elicits and models 32 algebraic notations, which are the common core of existing formal methods and modern programming languages. The extremely small set of formal notations has been proven sufficient for modeling and specifying real-time systems, their architecture, and static/dynamic behaviors in real-world software engineering environment.

Parametric approach to the specification and analysis of real-time scheduling based on ACSR-VP

This paper describes an approach to the specification and analysis of scheduling problems of real-time systems. The method is based on Algebra of Communicating Shared Resources with Value-Passing (ACSR-VP), which is an extension of ACSR, a real-time process algebra, with value-passing capabilities and parameterized processes. ACSR-VP is used to describe an instance of a scheduling problem as a process that has parameters of the problem as free variables. The specification is analyzed by means of a symbolic algorithm, and a boolean expression with free variables is produced as an outcome of the analysis. The solution to a boolean expression identifies under what values of the unknown parameters the system becomes schedulable. The paper presents the theory of ACSR-VP briefly and an example of the period assignment problem for rate-monotonic scheduling. We also explain our current tool implementation effort and plan for incorporating it into the existing toolset, PARAGON.

A real-time process algebra with open intervals and maximal progress

Many real-time process algebras have the maximal progress assumption. In those process algebras, the time intervals in which actions are enabled are left-closed. This paper presents a process algeb...

Real time process algebra with time-dependent conditions

We add conditionals with time-dependent conditions to the real time process algebra with parametric timing from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 10]. This extension facilitates flexible dependence of process behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier in a discrete time setting by Baeten and Bergstra [Formal Aspects of Computing 8 (1996) 188–208].

Metric semantics for true concurrent real time

This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langerak's bundle event structures, a variant of Winskel's event structures. The distance function of the metric is based on the amount of time to which event structures do ‘agree’. We show that this intuitive notion of distance is a pseudo-metric (but not a metric) on the set of timed event structures. A generalisation to equivalence classes of timed event structures in which we abstract from event identities and non-executable events (events that can never occur) is shown to be a complete ultra-metric space. We present an operational semantics for the considered language and show that the metric semantics is an abstraction of it. The operational semantics is characterised by the absence of synchronisation on the advance of time as opposed to the operational semantics of most real-time calculi. The consistency between our metric and an existing cpo-based denotational semantics is briefly investigated.

Parametric Approach to the Specification and Analysis of Real-time System Designs based on ACSR-VP

This paper describes an approach to the specification and analysis of scheduling problems of real-time systems. The method is based on ACSR-VP, which is an extension of ACSR, a real-time process algebra, with value-passing capabilities and parameterized processes. ACSR-VP is used to describe an instance of a scheduling problem as a process that has parameters of the problem as free variables. The specification is analyzed by means of a symbolic algorithm, and a boolean expression with free variables is produced as an outcome of the analysis. The solution to a boolean expression identifies under what values of the unknown parameters the system becomes schedulable. The paper presents the theory of ACSR-VP briefly and an example of the period assignment problem for rate-monotonic scheduling. We also explain our current tool implementation effort and plan for incorporating it into the existing toolset, PARAGON.

A Complete Axiomatization of Finite-state ACSR Processes

A real-time process algebra, called ACSR, has been developed to facilitate the specification and analysis of real-time systems. ACSR 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-time 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. In addition to operators common to process algebra, ACSR includes the scope operator, which can be used to model timeouts and interrupts. Equivalence between ACSR terms is based on the notion of strong bisimulation. This paper briefly describes the syntax and semantics of ACSR and then presents a set of algebraic laws that can be used to prove equivalence of ACSR processes. The contribution of this paper is the soundness and completeness proofs of this set of laws. The completeness proof is for finite-state ACSR processes, which are defined to be processes without free variables under parallel operator or scope operator.

Real space process algebra

Abstract The real time process algebra of Baeten and Bergstra [ Formal Aspects of Computing , 3 , 142–188 (1991)] is extended to real space by requiring the presence of spatial coordinates for each atomic action, in addition to the required temporal attribute. It is found that asynchronous communication cannot easily be avoided. Based on the state operators of Baeten and Bergstra [ Information and Computation , 78 , 205–245 (1988)] and following Bergstra et al. [ Proc. Seminar on Concurrency , LNCS 197, Springer, 1985, pp. 76–95], asychronous communication mechanisms are introduced as an additional feature of real space process algebra. The overall emphasis is on the introductory explanation of the features of real space process algebra, and characteristic examples are given for each of these.

Congruent weak bisimulation with dense real-time

New definitions for connectives in a real-time process algebra are introduced, for which the natural weak bisimulation relation is a congruence. Two kinds of weak bisimulation can be distinguished: step and path bisimulation.

Real time process algebra

Abstract We describe an axiom system ACP p that incorporates real timed actions. Many examples are provided in order to explain the intuitive contents of the notation. ACP p is a generalisation of ACP. This implies that some of the axioms have to be relaxed and that ACP can be recovered as a special case from it. The purpose of ACP p is to serve as a specification language for real time systems. The axioms of ACP p explain its operational meaning in an algebraic form.