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In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…
We consider the problem of computing the maximal probability of satisfying an omega-regular specification for stochastic nonlinear systems evolving in discrete time. The problem reduces, after automata-theoretic constructions, to finding…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an omega-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium…
We extend the formalism of Conjectural Variations games to Stackelberg games involving multiple leaders and a single follower. To solve these nonconvex games, a common assumption is that the leaders compute their strategies having perfect…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…
In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states.…
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…
We describe a new algorithm, the $(k,\ell)$-pebble game with colors, and use it obtain a characterization of the family of $(k,\ell)$-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs.…
We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
The family of $(k,\ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic problem is to decide whether a given…
We study the computational complexity of basic decision problems for one-counter simple stochastic games (OC-SSGs), under various objectives. OC-SSGs are 2-player turn-based stochastic games played on the transition graph of classic…
We consider a class of two-player zero-sum stochastic games with finite state and compact control spaces, which we call stochastic shortest path (SSP) games. They are undiscounted total cost stochastic dynamic games that have a cost-free…