**Equivalence semantics for concurrency: comparison and application**

**V.C. Galpin**

**Technical Report ECS-LFCS-98-397, PhD Thesis, Department of Computer Science, University of Edinburgh, 1998.**

**Abstract**

Since the development of CCS and other process algebras, many extensions to these process algebras have been proposed to model different aspects of concurrent computation. It is important both theoretically and practically to understand the relationships between these process algebras and between the semantic equivalences that are defined for them.

In this thesis, I investigate the comparison of semantic equivalences based on bisimulation which are defined for process algebras whose behaviours are described by structured operational semantics, and expressed as labelled transition systems. I first consider a hierarchy of bisimulations for extensions to CCS, using both existing and new results to describe the relationships between their equivalences with respect to pure CCS terms. I then consider a more general approach to comparison by investigating labelled transition systems with structured labels. I define bisimulation homomorphisms between labelled transition systems with different labels, and show how these can be used to compare equivalences.

Next, I work in the meta-theory of process algebras and consider a new format that is an extension of the \emph{tyft/tyxt} format for transition system specifications. This format treats labels syntactically instead of schematically, and hence I use a definition of bisimulation which requires equivalence between labels instead of exact matching. I show that standard results such as congruence and conservative extension hold for the new format.

I then investigate how comparison of equivalences can be approached through the notion of extension to transition system specifications. This leads to the main results of this study which show how in a very general fashion the bisimulations defined for two different process algebras can be compared over a subset of terms of the process algebras.

I also consider what implications the conditions which are required to obtain these results have for modelling process algebras, and show that these conditions do not impose significant limitations. Finally, I show how these results can be applied to existing process algebras. I model a number of process algebras with the extended format and derive new results from the meta-theory developed.

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