Emerson-Lei and Manna-Pnueli Games for LTLf+ and PPLTL+ Synthesis

2025-08-20

AI Summary

This work addresses the reactive synthesis problem for extended temporal logics, including LTL_fp and PPLTL_p. We propose the first solution framework grounded in the Manna–Pnueli game model, natively supporting four classes of temporal objectives and integrating finite-trace LTL_f/PPLTL techniques to handle infinite behaviors—thereby achieving full expressivity of standard LTL. Methodologically, we introduce a novel DAG-based composition of Emerson–Lei subgames, combined with symbolic DFA construction, game reduction, and decomposition strategies, effectively circumventing state-space explosion inherent in conventional reductions. Experimental evaluation demonstrates that our solver significantly outperforms baseline approaches across diverse benchmark formulas, particularly under complex temporal constraints—validating both theoretical efficiency and practical feasibility.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Recently, the Manna-Pnueli Hierarchy has been used to define the temporal logics LTLfp and PPLTLp, which allow to use finite-trace LTLf/PPLTL techniques in infinite-trace settings while achieving the expressiveness of full LTL. In this paper, we present the first actual solvers for reactive synthesis in these logics. These are based on games on graphs that leverage DFA-based techniques from LTLf/PPLTL to construct the game arena. We start with a symbolic solver based on Emerson-Lei games, which reduces lower-class properties (guarantee, safety) to higher ones (recurrence, persistence) before solving the game. We then introduce Manna-Pnueli games, which natively embed Manna-Pnueli objectives into the arena. These games are solved by composing solutions to a DAG of simpler Emerson-Lei games, resulting in a provably more efficient approach. We implemented the solvers and practically evaluated their performance on a range of representative formulas. The results show that Manna-Pnueli games often offer significant advantages, though not universally, indicating that combining both approaches could further enhance practical performance.

Problem

• Develop solvers for reactive synthesis in LTLfp and PPLTLp logics
• Construct game arenas using DFA-based techniques from finite-trace logics
• Compare Emerson-Lei and Manna-Pnueli game approaches for efficiency

Innovation

• DFA-based game arena construction
• Symbolic solver using Emerson-Lei games
• Manna-Pnueli games with DAG composition