Verification of Linear Duration Invariants by Model Checking CTL Properties

  • Authors:

  • Miaomiao Zhang;Dang Hung;Zhiming Liu

  • Affiliations:

  • School of Software Engineering, Tongji University, Shanghai, China;College of Technology, Vietnam National University, Hanoi, Vietnam;International Institute of Software Technology, United Nations University, Macau, China

  • Venue:
  • Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
  • Year:
  • 2008

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Abstract

Linear duration invariants (LDI) are important safety properties of real-time systems. They can be easily formulated in terms of a class of chop-free formulas in the Duration Calculus (DC). Compared to other temporal logics, the specification in DC is simpler, neater and more importantly easier to understand. However, directly model checking them is more difficult than model checking properties formulated in the computation tree logic (CTL). In this paper, we present a technique for the verification of the satisfaction of a LDI ${\cal D}$ by a timed automaton ${\cal A}$ by model checking a CTL property. For this, we construct an untimed automaton Gfrom ${\cal A}$, and prove that ${\cal A}$ satisfies ${\cal D}$ iff ${\cal D}$ is is satisfied by the set of all paths of G. To Verify that all paths of Gsatisfy ${\cal D}$, we construct a CTL formula 驴and simply check if Gsatisfies 驴. By this, we convert the problem of verification of the LDI to the problem of model checking CTL formula. As a result, the CTL model checking techniques and tools, such as UPPAAL, can be used for verification of LDI specified in the DC.