3 results
Thomas Colcombet ; Nathanaël Fijalkow ; Florian Horn.
We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is given by the size of the maximal antichain of left quotients […]
Published on January 29, 2024
Thomas Colcombet ; Nathanaël Fijalkow ; Paweł Gawrychowski ; Pierre Ohlmann.
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals: showing an equivalence and normalisation result between […]
Published on September 7, 2022
Nathanaël Fijalkow ; Martin Zimmermann.
We consider two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions generalize the corresponding classical omega-regular conditions […]
Published on June 26, 2014