Initial-state detectability and initial-state opacity of unambiguous weighted automata

Abstract

In this paper, we investigate the verification problem of initial-state detectability (I-detectability) and initial-state opacity (I-opacity) in discrete event systems modeled by unambiguous weighted automata. An I-observer is constructed so as to derive necessary and sufficient conditions for checking strong I-detectability, weak I-detectability, and I-opacity, with exponential complexity. In addition, an approach based on diagnosability analysis is proposed for verifying strong I-detectability. Compared with an I-observer-based approach, the diagnosability-based approach has a lower complexity, and in the case where all the unobservable events in an unambiguous weighted automaton are represented by a unique symbol, the diagnosability-based approach has polynomial complexity.