Efficient Verification of Metric Temporal Properties with Past in Pointwise Semantics

2025-10-16

AI Summary

This paper addresses the model checking problem for Metric Interval Temporal Logic (MITL) under pointwise semantics with past-tense operators. We propose the first efficient deterministic construction of timed automata supporting past modalities. Our method compiles the MITL past fragment into a network of deterministic timed automata in linear time, then extends it to full MITL—including both future and past modalities—via synchronized event-clock automata augmented with shared variables and future clocks, yielding a deterministic generalized timed automaton. To handle both finite and infinite traces uniformly, we integrate a liveness analysis algorithm based on strongly connected components. Experimental evaluation on 72 benchmark formulas and two classical real-time systems demonstrates end-to-end pointwise-semantics model checking, achieving significant performance improvements over state-of-the-art approaches.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• 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

Model checking for real-timed systems is a rich and diverse topic. Among the different logics considered, Metric Interval Temporal Logic (MITL) is a powerful and commonly used logic, which can succinctly encode many interesting timed properties especially when past and future modalities are used together. In this work, we develop a new approach for MITL model checking in the pointwise semantics, where our focus is on integrating past and maximizing determinism in the translated automata. Towards this goal, we define synchronous networks of timed automata with shared variables and show that the past fragment of MITL can be translated in linear time to synchronous networks of deterministic timed automata. Moreover determinism can be preserved even when the logic is extended with future modalities at the top-level of the formula. We further extend this approach to the full MITL with past, translating it into networks of generalized timed automata (GTA) with future clocks (which extend timed automata and event clock automata). We present an SCC-based liveness algorithm to analyse GTA. We implement our translation in a prototype tool which handles both finite and infinite timed words and supports past modalities. Our experimental evaluation demonstrates that our approach significantly outperforms the state-of-the-art in MITL satisfiability checking in pointwise semantics on a benchmark suite of 72 formulas. Finally, we implement an end-to-end model checking algorithm for pointwise semantics and demonstrate its effectiveness on two well-known benchmarks.

Problem

• Developing efficient MITL model checking for real-time systems
• Translating past temporal logic to deterministic timed automata
• Enhancing performance in pointwise semantics model checking

Innovation

• Translates MITL past fragment to deterministic timed automata
• Extends approach to full MITL using generalized timed automata
• Implements SCC-based liveness algorithm for GTA analysis