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

TL;DR

This paper introduces novel solvers for reactive synthesis in LTLf+ and PPLTL+ logics using Emerson-Lei and Manna-Pnueli games, demonstrating improved efficiency through graph-based techniques and practical evaluation.

Contribution

It presents the first solvers for these logics based on game-theoretic approaches, combining Emerson-Lei and Manna-Pnueli games for more efficient synthesis.

Findings

Manna-Pnueli games often outperform Emerson-Lei games in efficiency

The combined approach enhances practical performance in reactive synthesis

Solvers are implemented and evaluated on various formulas

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.