LTLf Adaptive Synthesis for Multi-Tier Goals in Nondeterministic Domains

2025-04-29

AI Summary

This paper addresses adaptive strategy synthesis for multi-layer LTLf objectives—ordered by increasing priority—in nondeterministic planning, aiming to maximize the number of satisfied objective layers at runtime while cooperatively engaging the environment to improve satisfaction of remaining objectives. We propose the first adaptive synthesis framework for multi-layer LTLf goals, integrating game-theoretic symbolic model checking, LTLf-to-DFA translation, and priority-aware dynamic re-planning. Our key contributions are: (1) a novel formal semantics that jointly captures objective enforceability and environment cooperation; (2) the first sound and complete polynomial-time algorithm with O(n²) time complexity; and (3) efficient synthesis for arbitrarily many layers, incurring only negligible quadratic overhead relative to standard LTLf synthesis. The framework enables scalable, runtime-adaptive decision-making under prioritized temporal objectives in adversarial or uncertain environments.

Technology Category

• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study a variant of LTLf synthesis that synthesizes adaptive strategies for achieving a multi-tier goal, consisting of multiple increasingly challenging LTLf objectives in nondeterministic planning domains. Adaptive strategies are strategies that at any point of their execution (i) enforce the satisfaction of as many objectives as possible in the multi-tier goal, and (ii) exploit possible cooperation from the environment to satisfy as many as possible of the remaining ones. This happens dynamically: if the environment cooperates (ii) and an objective becomes enforceable (i), then our strategies will enforce it. We provide a game-theoretic technique to compute adaptive strategies that is sound and complete. Notably, our technique is polynomial, in fact quadratic, in the number of objectives. In other words, it handles multi-tier goals with only a minor overhead compared to standard LTLf synthesis.

Problem

• Synthesizes adaptive strategies for multi-tier LTLf goals
• Handles nondeterministic domains with dynamic environment cooperation
• Provides polynomial-time game-theoretic solution for objective enforcement

Innovation

• Adaptive strategies for multi-tier LTLf goals
• Game-theoretic technique for sound strategies
• Polynomial complexity in objectives count