Hyper Partial Order Logic

Authors Béatrice Bérard, Stefan Haar, Loic Hélouët

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Béatrice Bérard
  • Sorbonne Université, CNRS, Laboratoire d'Informatique de Paris 6, LIP6, F-75005 Paris, France
Stefan Haar
  • INRIA and LSV, ENS Paris-Saclay and CNRS, Université Paris-Saclay, France
Loic Hélouët
  • Université de Rennes, Inria, CNRS, IRISA, France

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Béatrice Bérard, Stefan Haar, and Loic Hélouët. Hyper Partial Order Logic. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We define HyPOL, a local hyper logic for partial order models, expressing properties of sets of runs. These properties depict shapes of causal dependencies in sets of partially ordered executions, with similarity relations defined as isomorphisms of past observations. Unsurprisingly, since comparison of projections are included, satisfiability of this logic is undecidable. We then address model checking of HyPOL and show that, already for safe Petri nets, the problem is undecidable. Fortunately, sensible restrictions of observations and nets allow us to bring back model checking of HyPOL to a decidable problem, namely model checking of MSO on graphs of bounded treewidth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Partial orders
  • logic
  • hyper-logic


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