Combinatorics from Concurrency: the Nice Labelling Problem for Event Structures∗
نویسنده
چکیده
An event structures is a mathematical model of a concurrent process. It consists of a set of local events ordered by a causality relation and separated by a conflict relation. A global state, or configuration, is an order ideal whose elements are pairwise not in conflict. Configurations, ordered by subset inclusion, form a poset whose Hasse diagram codes the state-transition graph of the process. By labelling edges, the state-transition graph can be enriched with the structure of a deterministic concurrent automaton on some alphabet. The nice labelling problem asks to minimize the cardinality of the alphabet. In this talk we shall first introduce the nice labelling problem and show how it translates to a graph coloring problem. We shall then survey on the problem and present the results that are available to us nowadays. The survey will also be the occasion to point out new perspectives, open problems, and research paths.
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