Related papers: Graph Operations on Parity Games and Polynomial-Ti…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
In recent years, there has been a growing interest in games on graphs within the research community, fueled by their relevance in applications such as economics, politics, and epidemiology. This paper aims to comprehensively detail the…
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 consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a…
Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…
For some time the discrete strategy improvement algorithm due to Jurdzinski and Voge had been considered as a candidate for solving parity games in polynomial time. However, it has recently been proved by Oliver Friedmann that the strategy…
We investigate the interrelation between graph searching games and games with imperfect information. As key consequence we obtain that parity games with bounded imperfect information can be solved in PTIME on graphs of bounded DAG-width…
It is well-known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires…
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…
We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in…
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…
The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
We address the problem of solving parity games with imperfect information on finite graphs of bounded structural complexity. It is a major open problem whether parity games with perfect information can be solved in PTIME. Restricting the…
We investigate a cops and robber game on directed graphs, where the robber moves along the arcs of the graph, while the cops can select any position at each time step. Our main focus is on the cop number: the minimum number of cops required…
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…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game…