Infinite Trace Objectives with Finite Trace Techniques: Translating LTL to LTLf+

2026-08-03

AI Summary

Traditional approaches to handling Linear Temporal Logic (LTL) specifications in AI tasks require translating them into nondeterministic automata over infinite words and subsequently determinizing these automata—a process that is notoriously challenging both theoretically and in practice. This work proposes a novel methodology that circumvents these difficulties by translating LTL formulas into an expressively equivalent variant, LTLf+, which operates over finite traces and admits efficient determinization. We present the first complete translation from LTL to LTLf+, achieved by normalizing LTL formulas via the syntactic reactive fragment of the Manna–Pnueli hierarchy and then linearly mapping each component into LTLf+. The resulting LTL → LTLf+ → automaton pipeline matches the double-exponential time complexity of classical methods while seamlessly integrating a wealth of existing efficient LTLf+ reasoning techniques, thereby significantly extending the applicability of LTLf+ tools to traditional LTL problems.

Abstract

Linear Temporal Logic (LTL) is one of the most widely adopted languages for specifying temporal extended objectives in AI, with applications ranging from reactive synthesis to stochastic planning in Markov decision processes and reinforcement learning. Traditionally, solving any of these problems requires translating the LTL specification to a nondeterministic automata on infinite words and then determinizing it, a step that is notoriously difficult in theory and in practice. Recent work has introduced LTLf+, which lifts the finite-trace logic LTLf to infinite traces. LTLf+ has the same expressive power as LTL, yet it retains most of the crucial advantages of its base logic LTLf. Most reasoning in LTLf+ rests on finite automata on finite words, for which we have not only a canonical minimal representation but also an efficient determinization procedure. In this work we present the first translation from LTL to LTLf+. We first normalize an LTL formula into the syntactic reactivity fragment of the Manna-Pnueli hierarchy, to create the general fragment-based shape of LTLf+. We then present linear translations for each individual component of that fragment. As a consequence of this translation, the expanding body of techniques developed for LTLf+ now becomes available to many AI problems currently formulated in LTL. We further show that this comes at no asymptotic cost, as the pipeline from LTL to automaton via LTLf+ remains doubly exponential.

Problem

• LTL
• infinite traces
• automata determinization
• temporal logic
• AI planning

Innovation

• LTLf+
• finite automata
• temporal logic translation
• reactive synthesis
• determinization