The Mutex Paradigm of Concurrency

Concurrency can be studied at different yet consistent levels of abstraction: from individual behavioural observations, to more abstract concurrent histories which can be represented by causality structures capturing intrinsic, invariant dependencies between executed actions, to system level devices such as Petri nets or process algebra expressions. Histories can then be understood as sets of closely related observations (here step sequences of executed actions). Depending on the nature of the observed relationships between executed actions involved in a single concurrent history, one may identify different concurrency paradigms underpinned by different kinds of causality structures (e.g., the true concurrency paradigm is underpinned by causal partial orders with each history comprising all step sequences consistent with some causal partial order). For some paradigms there exist closely matching system models such as elementary net systems (en-systems) for the true concurrency paradigm, or elementary net systems with inhibitor arcs (eni-systems) for a paradigm where simultaneity of executed actions does not imply their unorderedness.In this paper, we develop a system model fitting the least restrictive concurrency paradigm and its associated causality structures. To this end, we introduce eni-systems with mutex arcs (enim-systems). Each mutex arc relates two transitions which cannot be executed simultaneously, but can be executed in any order. To link enim-systems with causality structures we develop a notion of process following a generic approach (semantical framework) which includes a method to generate causality structures from the new class of processes.