LTL to Deterministic Emerson-Lei Automata

TL;DR

This paper presents a novel method for translating linear temporal logic (LTL) into deterministic Emerson-Lei automata, improving automata size and efficiency by leveraging the automata's acceptance condition structure and component knowledge.

Contribution

It introduces a new translation approach from LTL to deterministic Emerson-Lei automata, utilizing a product construction and component knowledge to reduce state space and enhance succinctness.

Findings

The translation reduces automata size compared to existing methods.

The approach is effective on benchmarks and probabilistic model checking cases.

Implementation in the Delag tool demonstrates practical applicability.

Abstract

We introduce a new translation from linear temporal logic (LTL) to deterministic Emerson-Lei automata, which are omega-automata with a Muller acceptance condition symbolically expressed as a Boolean formula. The richer acceptance condition structure allows the shift of complexity from the state space to the acceptance condition. Conceptually the construction is an enhanced product construction that exploits knowledge of its components to reduce the number of states. We identify two fragments of LTL, for which one can easily construct deterministic automata and show how knowledge of these components can reduce the number of states. We extend this idea to a general LTL framework, where we can use arbitrary LTL to deterministic automata translators for parts of formulas outside the mentioned fragments. Further, we show succinctness of the translation compared to existing construction. The construction is implemented in the tool Delag, which we evaluate on several benchmarks of LTL formulas and probabilistic model checking case studies.