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

arXiv: https://arxiv.org/abs/2508.14725 · HTML: https://mlsanity.com/paper/2508.14725/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications](https://mlsanity.com/paper/1911.08145/) (2019)
- [LTLf Synthesis with Fairness and Stability Assumptions](https://mlsanity.com/paper/1912.07804/) (2019)
- [A Symbolic Approach to Safety LTL Synthesis](https://mlsanity.com/paper/1709.07495/) (2017)
- [LTLf+ and PPLTL+: Extending LTLf and PPLTL to Infinite Traces](https://mlsanity.com/paper/2411.09366/) (2024)

## Built on by (most cited first, 2 of 2)

- [Symbolic Synthesis for LTLf+ Obligations](https://mlsanity.com/paper/2604.18532/) (2026)
- [Infinite Trace Objectives with Finite Trace Techniques: Translating LTL to LTLf+](https://mlsanity.com/paper/2608.02454/) (2026)

## Abstract (arXiv)

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.