Better Quality in Synthesis through Quantitative Objectives

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.

Bridging boolean and quantitative synthesis using smoothed proof search

“…Quantitative synthesis has been studied in the past by the automata-theoretic synthesis community [3][4][5][6]. Specifically, the statement for our problem is derived from prior work by Chatterjee et al [6].…”

“…However, there can be many implementations that meet these properties, and some of them are more desirable than others. Given this, it is appropriate to consider synthesis tasks where the synthesized implementation must not only meet a boolean specification, but also be optimal with respect to a quantitative objective [3,6].…”

Synthesizing Controllers for Automation Tasks with Performance Guarantees

“…Admittedly, efforts within the research community target to synthesize optimal controllers [1,8,2,4]. Nevertheless, we argue that finding optimal controllers can be difficult in practice -apart from complexity considerations, the optimality criteria are often multiple yet independent measures and no global optimum exists in general.…”

“…For parallel execution, MGSyn automatically derives action PAR belt-move belt-move(dev 1 , wp 1 , pos 1a , pos 1b , dev 2 , wp 2 , pos 2a , pos 2b ) for moving two different work pieces on two different conveyor belts at the same time. In the precondition of this action, the constraints dev 1 = dev 2 , wp 1 = wp 2 , pos 1a = pos 2a , pos 2b and pos 1b = pos 2a , pos 2b are automatically added to ensure that parameter values are different 1 .…”

Energy and Mean-Payoff Games with Imperfect Information

“…This problem has tight connection (through polynomial-time reductions) with important theoretical questions about logics and games, such as the µ-calculus model-checking, and solving parity games [13,14,17,18]. Second, quantitative objectives in general are gaining interest in the specification and design of reactive systems [8,5,11], where the weights represent resource usage (e.g., energy consumption or network usage); the problem of controller synthesis with resource constraints requires the solution of quantitative games [20,6,1,3]. Finally, mean-payoff games are log-space equivalent to energy games (EG) where the objective of Player 1 is to maintain the sum of the weight (called the energy level) positive, given a fixed initial credit of energy.…”