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

TL;DR

This paper introduces a novel translation from MITL to generalized timed automata (GTA) that improves efficiency and presents a new zone-based liveness algorithm for GTAs, enabling effective model checking despite the lack of finite bisimulation.

Contribution

It offers a concise MITL to GTA translation with exponential improvements and develops the first zone-based liveness algorithm for GTAs, overcoming fundamental challenges.

Findings

Exponential improvement in translating the timed until modality.

New zone-based algorithm for Buchi non-emptiness in GTAs.

Reduction of MITL model checking to GTA liveness checking.

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.