Parametric disjunctive timed networks

2025-12-04

AI Summary

This paper investigates two reachability problems in parametric disjunctive timed networks: *local* reachability (existence of a parameter valuation enabling at least one process to reach a target location) and *global* reachability (existence of a parameter valuation enabling all processes to simultaneously reach their target locations). We consider single-clock discrete-time automata with location-guarded communication. Our method combines zone abstraction with counterexample-guided parameter-space partitioning. We establish, for the first time, the decidability of local reachability in single-clock systems without invariants—thereby revealing the critical role of invariants in expressive power. We precisely characterize undecidability boundaries for global reachability and for local reachability in the presence of invariants. Furthermore, we identify novel decidable subclasses under syntactically restricted conditions. Collectively, these results advance the theoretical foundations and practical applicability of formal verification for parametric real-time systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Local Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We consider distributed systems with an arbitrary number of processes, modelled by timed automata that communicate through location guards: a process can take a guarded transition if at least one other process is in a given location. In this work, we introduce parametric disjunctive timed networks, where each timed automaton may contain timing parameters, i.e. unknown constants. We investigate two problems: deciding the emptiness of the set of parameter valuations for which 1) a given location is reachable for at least one process (local property), and 2) a global state is reachable where all processes are in a given location (global property). Our main positive result is that the first problem is decidable for networks of processes with a single clock and without invariants; this result holds for arbitrarily many timing parameters -- a setting with few known decidability results. However, it becomes undecidable when invariants are allowed, or when considering global properties, even for systems with a single parameter. This highlights the significant expressive power of invariants in these networks. Additionally, we exhibit further decidable subclasses by restraining the syntax of guards and invariants.

Problem

• Deciding parameter valuations for local reachability in timed networks
• Investigating decidability of global state reachability with parameters
• Analyzing impact of invariants on decidability in parametric systems

Innovation

• Parametric timed automata with location guards
• Decidability for single-clock systems without invariants
• Undecidability introduced by invariants or global properties