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[工程科技]Towards a homotopy theory of process algebra
TOWARDS A HOMOTOPY THEORY OF PROCESS ALGEBRA
8 PHILIPPE GAUCHER
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2 Abstract. This paper proves that labelled flows are expressive enough to contain all pro-
cess algebras which are a standard model for concurrency. More precisely, we construct
y the space of execution paths and of higher dimensional homotopies between them for every
a
process name of every process algebra with any synchronization algebra using a notion of
M labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimen-
sional automata (HDA): one non-degenerate full n-dimensional cube (no more no less) in the
5
1 underlying space of the time flow corresponding to the concurrent execution of n actions.
This result will enable us in future papers to develop a homotopical approach of process
] algebras. Indeed, several homological constructions related to the causal structure of time
T flow are possible only in the framework of flows.
A
.
h
t
a Contents
m
[ 1. Introduction 1
4 2. Process algebra 3
v 3. Decorated σ-labelled precubical set 6
2 4. Denotational semantics using σ-labelled precubical sets 15
5 5. Restriction in dimension 1 and HDA paradigm 19
5
1 6. Decorated σ-labelle
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