Verification of Detectability for Unambiguous Weighted Automata Using Self-Composition

This paper aims to explore the problem of verifying detectability for unambiguous weighted automata (UWAs) through the utilization of modified self-composition. Specifically, we focus on two types of detectability: strong periodic detectability (SPD) and strong D-detectability (SDD). The problem involves periodically determining the current state or distinguishing certain state-pairs of the system, based on the occurrence of a finite number of observable events. We introduce a new polynomial-time algorithm different from the detector, called self-composition for UWAs, and prove that it can be used to verify the SPD and SDD for UWAs. Ultimately, we propose necessary and sufficient conditions based on modified self-composition techniques to verify the aforementioned detectabilities for the studied UWA.