Deciding detectability for labeled Petri nets

Abstract

Detectability of discrete event systems is a property to decide whether the current and subsequent states can be determined based on observations. We investigate the existence of algorithms for checking strong and weak detectability for systems modeled as labeled Petri nets. Strong detectability requires that we can always determine, after a finite number of observations, the current and subsequent markings of the system, while weak detectability requires that we can determine, after a finite number of observations, the current and subsequent markings for some trajectories of the system. We show that there is an algorithm to check strong detectability requiring exponential space, and that there is no algorithm to check weak detectability.