A Probabilistic Duration Calculus

  • Z. Liu
  • A. P. Ravn
  • E. V. Sørensen
  • C. Zhou
Part of the Dependable Computing and Fault-Tolerant Systems book series (DEPENDABLECOMP, volume 7)


This paper presents a calculus that enables a designer of an embedded, real-time system to reason about and calculate whether a given requirement will hold with a sufficient high probability for given failure probabilities for components used in the design of the system. The main idea is to specify requirements and design in Duration Calculus, a real-time, interval logic, to define satisfaction probabilities for formulas in this calculus, and establish a calculus with rules that support calculation of the probability for a composite formula from probabilities of its constituents. This ensures that reasoning about probabilities is consistent with requirements and design decisions. We thus avoid introducing separate models for requirements and reliability analysis. The system model is a finite automaton with fixed transition probabilities. This defines discrete Markov processes as basis for the calculus.

Key Words

duration calculus real-time systems probabilistic automata satisfaction probability 


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Copyright information

© Springer-Verlag/Wien 1993

Authors and Affiliations

  • Z. Liu
    • 1
  • A. P. Ravn
    • 2
  • E. V. Sørensen
    • 2
  • C. Zhou
    • 3
    • 4
  1. 1.Department of Computer ScienceUniversity of WarwickCoventryEngland, UK
  2. 2.Department of Computer ScienceTechnical University of DenmarkLyngbyDenmark
  3. 3.International Institute for Software TechnologyUnited Nations UniversityMacauChina
  4. 4.Software InstituteAcademia SinicaBeijingP.R. China

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