Approximation of a trace, asynchronous automata and the ordering of events in a distributed system
The notion of trace was introduced in order to modelize the concurrency of actions. A trace is an element of the quotient of the free monoid by the congruence generated by a finite set of relations of the form ab∼ba. We introduce the notion of the approximation of a trace and we study its properties. The main result is the existence of an asynchronous automaton which recognizes the set of traces corresponding to an approximation. We give two applications : the first one is a new proof of Zielonka's theorem, and the second one is an algorithm for the ordering of events in a distributed system.
KeywordsAsynchronous Automaton Recognizable Subset
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