# Symbolic Synthesis for LTLf+ Obligations

arXiv: https://arxiv.org/abs/2604.18532 · HTML: https://mlsanity.com/paper/2604.18532/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [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+ and PPLTL+: Extending LTLf and PPLTL to Infinite Traces](https://mlsanity.com/paper/2411.09366/) (2024)
- [Emerson-Lei and Manna-Pnueli Games for LTLf+ and PPLTL+ Synthesis](https://mlsanity.com/paper/2508.14725/) (2025)

## Built on by (most cited first, 1 of 1)

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

## Abstract (arXiv)

We study synthesis for obligation properties expressed in LTLfp, the extension of LTLf to infinite traces. Obligation properties are positive Boolean combinations of safety and guarantee (co-safety) properties and form the second level of the temporal hierarchy of Manna and Pnueli. Although obligation properties are expressed over infinite traces, they retain most of the simplicity of LTLf. In particular, we show that they admit a translation into symbolically represented deterministic weak automata (DWA) obtained directly from the symbolic deterministic finite automata (DFA) for the underlying LTLf properties on trace prefixes. DWA inherit many of the attractive algorithmic features of DFA, including Boolean closure and polynomial-time minimization. Moreover, we show that synthesis for LTLfp obligation properties is theoretically highly efficient - solvable in linear time once the DWA is constructed. We investigate several symbolic algorithms for solving DWA games that arise in the synthesis of obligation properties and evaluate their effectiveness experimentally. Overall, the results indicate that synthesis for LTLfp obligation properties can be performed with virtually the same effectiveness as LTLf synthesis.