Better Quality in Synthesis through Quantitative Objectives

TL;DR

This paper introduces a method for synthesizing optimal reactive system implementations by using quantitative objectives and automata with lexicographic mean-payoff conditions, enabling preference among solutions.

Contribution

It proposes a novel framework employing automata with lexicographic mean-payoff conditions for quantitative synthesis of reactive systems, along with algorithms for solving related graph games.

Findings

Automata with lexicographic mean-payoff conditions can express various quantitative properties.

Algorithms are developed for solving lexicographic mean-payoff and combined mean-payoff/parity games.

The approach enables synthesis of implementations optimized for quantitative criteria.

Abstract

Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the "goodness" of an implementation. Using games with corresponding quantitative objectives, we can synthesize "optimal" implementations, which are preferred among the set of possible implementations that satisfy a given specification. In particular, we show how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and the solution of games with both lexicographic mean-payoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games.