Minimisation of Event Structures

Authors Paolo Baldan , Alessandra Raffaetà

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Paolo Baldan
  • University of Padova, Italy
Alessandra Raffaetà
  • Ca' Foscari University of Venice, Italy

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Paolo Baldan and Alessandra Raffaetà. Minimisation of Event Structures. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Event structures are fundamental models in concurrency theory, providing a representation of events in computation and of their relations, notably concurrency, conflict and causality. In this paper we present a theory of minimisation for event structures. Working in a class of event structures that generalises many stable event structure models in the literature, (e.g., prime, asymmetric, flow and bundle event structures) we study a notion of behaviour-preserving quotient, taking hereditary history preserving bisimilarity as a reference behavioural equivalence. We show that for any event structure a uniquely determined minimal quotient always exists. We observe that each event structure can be seen as the quotient of a prime event structure, and that quotients of general event structures arise from quotients of (suitably defined) corresponding prime event structures. This gives a special relevance to quotients in the class of prime event structures, which are then studied in detail, providing a characterisation and showing that also prime event structures always admit a unique minimal quotient.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Software and its engineering → Formal methods
  • Event structures
  • minimisation
  • history-preserving bisimilarity
  • behaviour-preserving quotient


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