Languages of Higher-Dimensional Timed Automata

2024-01-30

Applications and Theory of Petri Nets

AI Summary

Modeling and inclusion checking for multi-event sets in real-time concurrent systems pose significant challenges due to the interplay of concurrency, timing constraints, and non-interleaving semantics. Method: This paper introduces the High-Dimensional Timed Automaton (HDTA) semantic framework, which uniquely integrates the non-interleaving concurrency model of high-dimensional automata with the clock-based timing mechanism of timed automata. Based on HDTAs, we define interval-timed pomsets with interfaces and establish their formal semantics. Contribution/Results: We prove that language inclusion for HDTAs is generally undecidable, yet becomes decidable upon time abstraction. Furthermore, a region construction method is developed, enabling practical verification tasks such as reachability analysis. This work provides a unified, rigorous, and more expressive mathematical foundation for precise modeling, verification, and analysis of real-time concurrent systems.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We present a new language semantics for real-time concurrency. Its operational models are higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional automata and timed automata. In real-time concurrent systems, both concurrency of events and timing and duration of events are of interest. Thus, HDTAs combine the non-interleaving concurrency model of higher-dimensional automata with the real-time modeling, using clocks, of timed automata. We define languages of HDTAs as sets of interval-timed pomsets with interfaces. We show that language inclusion of HDTAs is undecidable. On the other hand, using a region construction we can show that untimings of HDTA languages have enough regularity so that untimed language inclusion is decidable. On a more practical note, we give new insights on when practical applications, like checking reachability, might benefit from using HDTAs instead of classical timed automata.

Problem

• Real-time Processing
• Complex Event Patterns
• Inclusion Problem

Innovation

• High-Dimensional Temporal Automata
• Real-time Multi-event Processing
• Enhanced System State Verification