Active Prediction for Discrete Event Systems

Authors Stefan Haar , Serge Haddad , Stefan Schwoon , Lina Ye

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Author Details

Stefan Haar
  • INRIA, LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France
Serge Haddad
  • LSV, ENS Paris-Saclay, CNRS, INRIA, Université Paris-Saclay, France
Stefan Schwoon
  • LSV, ENS Paris-Saclay, CNRS, INRIA, Université Paris-Saclay, France
Lina Ye
  • LRI, Université Paris-Saclay, CentraleSupélec, France

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Stefan Haar, Serge Haddad, Stefan Schwoon, and Lina Ye. Active Prediction for Discrete Event Systems. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


A central task in partially observed controllable system is to detect or prevent the occurrence of certain events called faults. Systems for which one can design a controller avoiding the faults are called actively safe. Otherwise, one may require that a fault is eventually detected, which is the task of diagnosis. Systems for which one can design a controller detecting the faults are called actively diagnosable. An intermediate requirement is prediction, which consists in determining that a fault will occur whatever the future behaviour of the system. When a system is not predictable, one may be interested in designing a controller to make it so. Here we study the latter problem, called active prediction, and its associated property, active predictability. In other words, we investigate how to determine whether or not a system enjoys the active predictability property, i.e., there exists an active predictor for the system. Our contributions are threefold. From a semantical point of view, we refine the notion of predictability by adding two quantitative requirements: the minimal and maximal delay before the occurence of the fault, and we characterize the requirements fulfilled by a controller that performs predictions. Then we show that active predictability is EXPTIME-complete where the upper bound is obtained via a game-based approach. Finally we establish that active predictability is equivalent to active safety when the maximal delay is beyond a threshold depending on the size of the system, and we show that this threshold is accurate by exhibiting a family of systems fulfilling active predictability but not active safety.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Mathematics of computing → Discrete mathematics
  • Automata Theory
  • Partially observed systems
  • Diagnosability
  • Predictability


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