Dimming Relations for the Efficient Analysis of Concurrent Systems via Action Abstraction

We study models of concurrency based on labelled transition systems where abstractions are induced by a partition of the action set. We introduce dimming relations, i.e., notions of behavioural equivalence which are able to relate two models if they can match each other’s actions whenever they are in the same partition block. We show applicability to a number of situations of practical interest which are apparently heterogeneous but exhibit similar behaviors although manifested via different actions. Dimming relations make the models more homogeneous by collapsing such distinct actions into the same partition block. With our examples, we show how these abstractions permit reducing the state-space complexity from exponential to polynomial in the number of concurrent processes.