Domains of higher-dimensional automata

Abstract

We carry on the program set up in [GJ92] by giving constructions of “domains of higher-dimensional automata (HDA)” on which we can define the truly-concurrent semantics of parallel languages, much in the style of domain theory (see [GS90]). In [GJ92] we gave a semantics for CCS-like languages. In this article, we show how to extend the technique to languages with real states, while keeping nice algebraic definitions. In particular, we are still able to compute local invariants which can decide a few computational properties of interest. For being used as actual computational definitions, the semantics is denotational (i.e. compositional); for being precise enough when it comes to studying the dynamic behaviour of programs, the denotations are higher-dimensional automata, which are no more than an operational behaviour (in the style of operational semantics, see [Plo81]). We conclude by giving the semantics of a small shared-memory imperative language.