Maximum Realizability for Linear Temporal Logic Specifications

TL;DR

This paper introduces a method for synthesizing system implementations that optimally balance hard LTL specifications with soft safety properties, allowing for best-effort satisfaction when full compliance is impossible.

Contribution

It formalizes a quantitative semantics for safety specifications and develops a MaxSAT-based algorithm for optimal synthesis balancing hard and soft constraints.

Findings

Effective in robotics scenarios

Applicable to power distribution networks

Outperforms existing approaches in satisfaction levels

Abstract

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.