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Verification of Opacity and Diagnosability for Pushdown Systems

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  • Koichi Kobayashi
  • Kunihiko Hiraishi

Abstract

In control theory of discrete event systems (DESs), one of the challenging topics is the extension of theory of finite-state DESs to that of infinite-state DESs. In this paper, we discuss verification of opacity and diagnosability for infinite-state DESs modeled by pushdown automata (called here pushdown systems). First, we discuss opacity of pushdown systems and prove that opacity of pushdown systems is in general undecidable. In addition, a decidable class is clarified. Next, in diagnosability, we prove that under a certain assumption, which is different from the assumption in the existing result, diagnosability of pushdown systems is decidable. Furthermore, a necessary condition and a sufficient condition using finite-state approximations are derived. Finally, as one of the applications, we consider data integration using XML (Extensible Markup Language). The obtained result is useful for developing control theory of infinite-state DESs.

Suggested Citation

  • Koichi Kobayashi & Kunihiko Hiraishi, 2013. "Verification of Opacity and Diagnosability for Pushdown Systems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, May.
    • Handle: RePEc:hin:jnljam:654059
    DOI: 10.1155/2013/654059
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