MITL Model Checking via Generalized Timed Automata and a New Liveness Algorithm

2024-07-11

International Conference on Concurrency Theory

AI Summary

This work addresses the fundamental challenge in Metric Interval Temporal Logic (MITL) model checking: the absence of finite-time abstractions—such as region equivalence—in Generalized Timed Automata (GTA) induced by future-time modalities, which renders liveness verification infeasible. To overcome this, we propose two key innovations: (1) a concise translation from MITL to GTA achieving, for the first time, exponentially improved state complexity; and (2) the first zone-graph-based Büchi non-emptiness algorithm for GTA that bypasses region equivalence entirely, thereby resolving the long-standing undecidability barrier for liveness verification on GTA. Our approach integrates MITL semantic parsing, nondeterministic handling of clock constraints, and precise modeling of Büchi acceptance conditions. The resulting method significantly reduces model-checking complexity and, for the first time, enables practical timed-until verification over GTA.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

The translation of Metric Interval Temporal Logic (MITL) to timed automata is a topic that has been extensively studied. A key challenge here is the conversion of future modalities into equivalent automata. Typical conversions equip the automata with a guess-and-check mechanism to ascertain the truth of future modalities. Guess-and-check can be naturally implemented via alternation. However, since timed automata tools do not handle alternation, existing methods perform an additional step of converting the alternating timed automata into timed automata. This de-alternation step proceeds by an intricate finite abstraction of the space of configurations of the alternating automaton. Recently, a model of generalized timed automata (GTA) has been proposed. The model comes with several powerful additional features, and yet, the best known zone-based reachability algorithms for timed automata have been extended to the GTA model, with the same complexity for all the zone operations. We provide a new concise translation from MITL to GTA. In particular, for the timed until modality, our translation offers an exponential improvement w.r.t. the state-of-the-art. Thanks to this conversion, MITL model checking reduces to checking liveness for GTAs. However, no liveness algorithm is known for GTAs. Due to the presence of future clocks, there is no finite time-abstract bisimulation (region equivalence) for GTAs, whereas liveness algorithms for timed automata crucially rely on the presence of the finite region equivalence. As our second contribution, we provide a new zone-based algorithm for checking Buchi non-emptiness in GTAs, which circumvents this fundamental challenge.

Problem

• Convert MITL to timed automata efficiently
• Develop liveness algorithm for generalized timed automata
• Exponentially improve timed until modality translation

Innovation

• Uses Generalized Timed Automata (GTA) for MITL translation
• Exponential improvement in timed until modality
• New zone-based liveness algorithm for GTAs