Description du projet
Des enchevêtrements pour les jeux de parité
L’un des principaux objectifs de l’informatique est de garantir que les systèmes informatiques sont formellement corrects en développant des méthodes permettant de prouver qu’un système met correctement en œuvre certaines propriétés données. Dans ce contexte, les jeux de parité constituent un défi. Ils constituent également un sujet de choix pour l’informatique théorique, car on pense qu’ils font partie de la classe de complexité P – une question qui se pose depuis deux décennies. Le projet PIGGY, financé par l’UE, se concentre sur la compréhension de la complexité inhérente à la résolution algorithmique des jeux de parité. L’exploration de la structure des enchevêtrements est au cœur même de l’étude.
Objectif
Virtually all aspects of society, industry and science are significantly impacted by increasingly complex computers and the software that they run. A major objective within computer science is to ensure that these computer systems are formally correct by developing ways to prove that a system correctly implements certain given properties, or ways to construct such a system. In this domain of computer science, an important topic is parity games. Many real-world systems run continuously and properties for such systems are described in temporal logics such as linear temporal logic (LTL) and various logics derived from or related to LTL. Solving parity games computes whether a given system has a property specified in these temporal logics, or constructs a system that implements such a property.
Parity games are in addition a compelling subject for theoretical computer science because they are believed to be in the complexity class P; however, this has been an open question for over 20 years. In recent years, new algorithms have been discovered that solve parity games in quasi-polynomial time, while at the same time researchers have found quasi-polynomial lower bounds for several families of algorithms.In my publication on tangle learning, I propose the notion of a tangle and show that existing parity game solving algorithm implicitly explore tangles when reasoning about how a player can force the opponent to move through the parity game from A to B.
The aim of this proposal is to understand the inherent complexity of solving parity games algorithmically. The strategy to achieve this is to obtain fundamental insights into the structure of tangles, how they are handled by parity game solving algorithms and how they arise in practical games.
Champ scientifique
Programme(s)
Régime de financement
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
7522 NB Enschede
Pays-Bas