Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

Model-checking Quantitative Alternating-time Temporal Logic on One-counter Game Models

We consider quantitative extensions of the alternating-time temporal logics ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in which the value of a counter can be compared to constants using equality, inequality and modulo constraints. We interpret these logics in one-counter game models which are infinite duration games played on finite control graphs where each transition can increase or decrease the value of an unbounded counter. That is, the state-space of these games are, generally, infinite. We consider the model-checking problem of the logics QATL and QATLs on one-counter game models with VASS semantics for which we develop algorithms and provide matching lower bounds. Our algorithms are based on reductions of the model-checking problems to model-checking games. This approach makes it quite simple for us to deal with extensions of the logical languages as well as the infinite state spaces. The framework generalizes on one hand qualitative problems such as ATL/ATLs model-checking of finite-state systems, model-checking of the branching-time temporal logics CTL and CTLs on one-counter processes and the realizability problem of LTL specifications. On the other hand the model-checking problem for QATL/QATLs generalizes quantitative problems such as the fixed-initial credit problem for energy games (in the case of QATL) and energy parity games (in the case of QATLs). Our results are positive as we show that the generalizations are not too costly with respect to complexity. As a byproduct we obtain new results on the complexity of model-checking CTLs in one-counter processes and show that deciding the winner in one-counter games with LTL objectives is 2ExpSpace-complete.Comment: 22 pages, 12 figure

Quantitative games with interval objectives

Traditionally quantitative games such as mean-payoff games and discount sum games have two players -- one trying to maximize the payoff, the other trying to minimize it. The associated decision problem, "Can Eve (the maximizer) achieve, for example, a positive payoff?" can be thought of as one player trying to attain a payoff in the interval $(0,\infty)$. In this paper we consider the more general problem of determining if a player can attain a payoff in a finite union of arbitrary intervals for various payoff functions (liminf, mean-payoff, discount sum, total sum). In particular this includes the interesting exact-value problem, "Can Eve achieve a payoff of exactly (e.g.) 0?"Comment: Full version of CONCUR submissio

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

How to Handle Assumptions in Synthesis

The increased interest in reactive synthesis over the last decade has led to many improved solutions but also to many new questions. In this paper, we discuss the question of how to deal with assumptions on environment behavior. We present four goals that we think should be met and review several different possibilities that have been proposed. We argue that each of them falls short in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493

Strategy Synthesis for Multi-dimensional Quantitative Objectives

Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express $\omega$-regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on VASS (vector addition systems with states). Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.Comment: Conference version published in CONCUR 2012, LNCS 7454. Journal version published in Acta Informatica, volume 51, issue 3-4, Springer, 201