An algebraic model of observable properties in distributed systems

Abstract

We propose orthomodular posets, algebraic models of quantum logic, as a formal tool in concurrency theory. We discuss their characteristics and study mutual relations with two other models of distributed systems: condition event net systems, a basic class of Petri nets, and the transition systems modelling CE net system behaviour. Central results are an adjointness situation among the three models and a strict relationship between fundamental notions in the different considered frameworks such as the relations of incompatibility and concurrency. Furthermore, substructures of orthomodular posets, like Boolean subalgebras or centres are interpreted, respectively, as state machine components of CE net systems or synchronization structures.