Reactive Synthesis with Maximum Realizability of Linear Temporal Logic Specifications

TL;DR

This paper introduces an optimization approach for reactive synthesis from LTL specifications, aiming to produce controllers that satisfy hard properties while minimally violating soft ones, using a novel maximum satisfiability encoding.

Contribution

It develops a new maximum satisfiability encoding for optimal reactive synthesis from LTL, incorporating a value function to quantify violations and iteratively searches for minimal violations within size bounds.

Findings

Effective encoding for optimal implementation search.

Iterative size-bound increase improves violation minimization.

Framework handles large sets of specifications.

Abstract

A challenging problem for autonomous systems is to synthesize a reactive controller that conforms to a set of given correctness properties. Linear temporal logic (LTL) provides a formal language to specify the desired behavioral properties of systems. In applications in which the specifications originate from various aspects of the system design, or consist of a large set of formulas, the overall system specification may be unrealizable. Driven by this fact, we develop an optimization variant of synthesis from LTL formulas, where the goal is to design a controller that satisfies a set of hard specifications and minimally violates a set of soft specifications. To that end, we introduce a value function that, by exploiting the LTL semantics, quantifies the level of violation of properties. Inspired by the idea of bounded synthesis, we fix a bound on the implementation size and search for an implementation that is optimal with respect to the said value function. We propose a novel maximum satisfiability encoding of the search for an optimal implementation (within the given bound on the implementation size). We iteratively increase the bound on the implementation size until a termination criterion, such as a threshold over the value function, is met.