Copyright © 2013 Koichi Kobayashi and Kunihiko Hiraishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.