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Towards an Algebra of Abstractions for Communicating Processes

Lookup NU author(s): Professor Maciej KoutnyORCiD, Dr Marta Koutny



It is often desirable to describe the interface of an implementation system at a different (usually more detailed) level of abstraction to the interface of the relevant specification. This calls for a relation aimed at formalising the notion that a process is an acceptable implementation of another target process in the event that they possess different interfaces. We conduct our investigation in the standard failures-divergences CSP process model, formulating a suitable implementation relation between the observable behaviours of the implementation and the target process. Interface difference and bridging is modelled by endowing the implementation relation with parameters, called extraction patterns, instrumental to interpreting implementation behaviour as target behaviour. Reasonable notions of implementation and extraction patterns should result in a relation satisfying the realisability and compositionality properties. The former means that, if target and implementation in fact have the same interface, then the implementation relation between them collapses into the standard implementation pre-order of CSP. Compositionality allows a target composed of several connected systems to be implemented by connecting their respective implementations. With respect to previous work, here we lift a restriction that prevented broadcast and other group communication to be modelled, and do without any constraint (other than divergence freedom) on admissible specification processes. Moreover, distributivity of the implementation relation over the network composition operator, i.e., compositionality, is extended to other useful process building operators, such as choice. Our novel approach is based on introducing operations over extraction patterns, mimicking (and being compatible with) operations over processes. We feel this constitutes a first step in the development of an algebra of abstraction for communicating processes in the CSP model.

Publication metadata

Author(s): Koutny M, Pappalardo G, Pietkiewicz-Koutny M

Publication type: Report

Publication status: Published

Series Title: School of Computing Science Technical Report Series

Year: 2006

Pages: 13

Print publication date: 01/02/2006

Source Publication Date: February 2006

Report Number: 949

Institution: School of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne