2006 | OriginalPaper | Buchkapitel
A Lattice-Theoretic Model for an Algebra of Communicating Sequential Processes
verfasst von : Malcolm Tyrrell, Joseph M. Morris, Andrew Butterfield, Arthur Hughes
Erschienen in: Theoretical Aspects of Computing - ICTAC 2006
Verlag: Springer Berlin Heidelberg
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We present a new lattice-theoretic model for communicating sequential processes. The model underpins a process algebra that is very close to CSP. It differs from CSP “at the edges” for the purposes of creating an elegant algebra of communicating processes. The one significant difference is that we postulate additional distributive properties for external choice. The shape of the algebra that emerges suggests a lattice-theoretic model, in contrast to traditional trace-theoretic models. We show how to build the new model in a mathematically clean step-by-step process. The essence of our approach is to model simple processes (i.e. those without choice, parallelism, or recursion) as a poset
S
of sequences, and then order-embed
S
into a complete (and completely distributive) lattice called the
free completely distributive lattice
over
S
. We explain the technique in detail and show that the resulting model does indeed capture our algebra of communicating sequential processes. The focus of the paper is not on the algebra per se, but on the model and the soundness of the algebra.