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Mutex Causality in Processes and Traces of General Elementary Nets
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Professor Maciej Koutny
Kleijn J, Koutny M
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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. In this paper, we present a system model fitting the least restrictive concurrency paradigm and its associated causality structures. To this end, we study elementary net systems with inhibitor and mutex arcs (ENIM-systems). 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. To complete the picture, we give a description of the abstract behaviour of ENIM-system in terms of suitable quotient monoids of step sequences, following the an approach in which individual observations underpinned by the same causality structure are grouped together to form a trace. In doing so, we demonstrate that static (structural) relationships between ENIM-system's transitions determine the equations underlying the congruences in the quotient monoid. The equivalence classes (elements of the quotient monoid) corresponding to ENIM-system's runs correspond exactly to the causal (relational) structures underlying processes.
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