First Steps in the Construction of the Geometric Machine Model

Abstract

This work introduces the Geometric Machine (GM) – a computational model for the construction and representation of concurrent and non-deterministic processes, preformed in a synchronized way, with infinite memory whose positions are labelled by the points of a geometric space. The ordered structure of the GM model is based on Girard’s Coherence Spaces. Starting with a coherence space of elementary processes, the inductive domain-theoretic structure of this model is step-wise and systematically constructed and the procedure completion ensures the existence of temporally and spatially infinite computations. A particular aim of our work is to apply this coherence-space-based interpretation to the semantic modelling parallelism and distributed computation over array structures.