2009/04/17 by Roderick Bloem, Krishnendu Chatterjee, Bloem, Roderick +5 · 5 citations
Computer Science · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Model-Driven Software Engineering Techniques #Software Testing and Debugging Techniques
paper · pdf · doi:10.48550/arxiv.0904.2638
openalex publication_date 2009/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.