Solving MDPs with LTLf+ and PPLTL+ Temporal Objectives

2025-05-22

AI Summary

This paper addresses the policy synthesis problem for Linear Temporal Logic over finite traces (LTLf⁺) and Probabilistic Propositional Linear Temporal Logic (PPLTL⁺) specifications on infinite trajectories of Markov Decision Processes (MDPs). We propose an efficient, scalable, and fully automated synthesis method. Our core contribution is the first integration of LTLf⁺/PPLTL⁺ into MDP planning, enabled by a novel class of deterministic finite automata (DFAs) tailored for probabilistic systems—“MDP-friendly” DFAs with controllable nondeterminism—that jointly ensure semantic fidelity, construction efficiency, and modular composability. The method integrates temporal-logic semantics translation, symbolic DFA construction, and probabilistic model checking to yield a lightweight, theoretically complete synthesis algorithm. Compared to conventional reactive synthesis, our approach substantially reduces state-space complexity and supports efficient symbolic implementation, thereby enhancing both scalability and practical applicability without sacrificing formal guarantees.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Multiagent Systems: Multiagent Planning
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The temporal logics LTLf+ and PPLTL+ have recently been proposed to express objectives over infinite traces. These logics are appealing because they match the expressive power of LTL on infinite traces while enabling efficient DFA-based techniques, which have been crucial to the scalability of reactive synthesis and adversarial planning in LTLf and PPLTL over finite traces. In this paper, we demonstrate that these logics are also highly effective in the context of MDPs. Introducing a technique tailored for probabilistic systems, we leverage the benefits of efficient DFA-based methods and compositionality. This approach is simpler than its non-probabilistic counterparts in reactive synthesis and adversarial planning, as it accommodates a controlled form of nondeterminism (``good for MDPs") in the automata when transitioning from finite to infinite traces. Notably, by exploiting compositionality, our solution is both implementation-friendly and well-suited for straightforward symbolic implementations.

Problem

• Extending LTLf+ and PPLTL+ to solve MDPs with temporal objectives
• Leveraging DFA-based methods for probabilistic systems efficiently
• Simplifying nondeterminism handling in automata for infinite traces

Innovation

• Leverages LTLf+ and PPLTL+ for MDPs
• Uses efficient DFA-based probabilistic techniques
• Exploits compositionality for symbolic implementations