Relational structures for concurrent behaviours

Relational structures based on acyclic relations can successfully model fundamental aspects of concurrent systems behaviour. Examples include Elementary Net systems and Mazurkiewicz traces. There are however cases where more general relational structures are needed. In this paper, we present a general model of relational structures which can be used for a broad class of concurrent behaviours. We demonstrate how this general set-up works for combined order structures which are based on two relations, viz. an acyclic ‘before’ relation and a possibly cyclic ‘not later than’ relation.