Reduction of Order Structures

Abstract

Relational order structures are used to describe and investigate properties of concurrent systems. To reduce the complexity of order structures, one typically considers only their essential components, which, in the case of partial orders, leads to the notion of Hasse diagrams. We lift this notion to the level of generalised mutex order structures, which are used to model not only causal dependencies but also weak causality and mutual exclusion. We provide a new and more concise axiomatic definition of these structures, investigate their important properties, and present efficient algorithms for computing their reduction and closure. The algorithms are implemented in a publicly available software tool with graphical user interface.