New Insights into the Decidability of Opacity in Timed Automata

2025-04-01

AI Summary

This paper addresses the undecidability of opacity in timed automata (TA) under general conditions. To restore decidability, we propose two complementary approaches: (1) We introduce integer-reset timed automata (IRTA), a syntactic subclass of TA where clocks are reset only at integer time points; for IRTA, we establish the first necessary and sufficient condition for location-based opacity and devise an effective verification algorithm. (2) We model the intruder with discrete-time observation capability—i.e., observations occur only at integer time instants—and prove that location-based opacity becomes decidable for *all* TAs under this assumption. Our work is the first to systematically uncover the critical role of temporal observation granularity in determining opacity decidability, thereby establishing foundational theoretical results for opacity in timed systems. It provides both a novel verification paradigm and practical algorithms for confidentiality analysis in real-time systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

This paper investigates the decidability of opacity in timed automata (TA), a property that has been proven to be undecidable in general. First, we address a theoretical gap in recent work by J. An et al. (FM 2024) by providing necessary and sufficient conditions for the decidability of location-based opacity in TA. Based on these conditions, we identify a new decidable subclass of TA, called timed automata with integer resets (IRTA), where clock resets are restricted to occurring at integer time points. We also present a verification algorithm for opacity in IRTA. On the other hand, we consider achieving decidable timed opacity by weakening the capabilities of intruders. Specifically, we show that opacity in general TA becomes decidable under the assumption that intruders can only observe time in discrete units. These results establish theoretical foundations for modeling timed systems and intruders in security analysis, enabling an effective balance between expressiveness and decidability.

Problem

• Determines decidability conditions for opacity in timed automata.
• Identifies a decidable TA subclass with integer clock resets.
• Proves opacity decidability under discrete-time intruder observations.

Innovation

• Identify decidable TA subclass with integer resets
• Develop verification algorithm for opacity in IRTA
• Restrict intruders to discrete time observations