Related papers: Solving Parity Games on Integer Vectors
Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science. Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space $\omega^\omega$. We consider such…
We provide a generic decision procedure for energy games with energy-bounded attacker and reachability objective, moving beyond vector-valued energies and vector-addition updates. All we demand is that energies form well-founded bounded…
Parity games can be used to represent many different kinds of decision problems. In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an…
We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…
In recent work, Watanabe, Eberhart, Asada, and Hasuo have shown that parity games can be seen as string diagrams, that is, as the morphisms of a symmetric monoidal category, an algebraic structure with two different operations of…
The solution of parity games over pushdown graphs (Walukiewicz '96) was the first step towards an effective theory of infinite-state games. It was shown that winning strategies for pushdown games can be implemented again as pushdown…
Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…
We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, for the case where the players are restricted to finite-memory strategies. First, we describe a general framework, where…
We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…
We study minimum integer representations of weighted games, i.e., representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the…
We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…
Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with…