# Maximum Realizability for Linear Temporal Logic Specifications

arXiv: https://arxiv.org/abs/1804.00415 · HTML: https://mlsanity.com/paper/1804.00415/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2018.

## Built on by (most cited first, 3 of 3)

- [Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles](https://mlsanity.com/paper/2212.03323/) (2022)
- [Omega-Regular Decision Processes](https://mlsanity.com/paper/2312.08602/) (2023)
- [Multi-Property Synthesis](https://mlsanity.com/paper/2601.10651/) (2026)

## Abstract (arXiv)

Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning, control of autonomous systems, and load distribution in power networks. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system's objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the "best-effort" satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of the bounded synthesis approach, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the safety specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.