Mutex Causality in Processes and Traces of General Elementary Nets

A concurrent history represented by a causality structure that captures the intrinsic, invariant dependencies between its actions, can be interpreted as defining a set of closely related observations (e.g., step sequences). Depending on the relationships observed in the histories of a system, the concurrency paradigm to which it adheres may be identified, with different concurrency paradigms underpinned by different kinds of causality structures. Elementary net systems with inhibitor arcs and mutex arcs (ENIM-systems) are a system model that through its process semantics and associated causality structures fits the least restrictive concurrency paradigm. One can also investigate the abstract behaviour of an ENIM-system by grouping together step sequences in equivalence classes (generalised comtraces) using the structural relations between its transitions. The resulting concurrent histories of the ENIM-system are consistent with the generalised stratified order structures underlying its processes. The paper establishes a link between ENIM-systems and trace theory allowing one to discuss different observations of concurrent behaviour in a way that is consistent with the causality semantics defined by the operationally defined processes.