Description du projet
Les conjectures secondaires de la complexité à grain fin: mise à niveau ou rejet
La théorie de la complexité informatique est une branche des mathématiques qui fait la distinction entre les solutions algorithmiques relativement efficaces et celles qui sont irréalisables. La théorie de la complexité à grain fin cherche à améliorer la «résolution» de ces distinctions, en proposant une détermination quantitative et, éventuellement, un aperçu de la complexité exacte des problèmes «difficiles» sur le plan informatique. Il existe trois conjectures primaires en vertu desquelles de nombreux résultats de dureté sont valables. Dix autres conjectures secondaires existent; il peut s’agir de variantes plus fortes, nous permettant de prouver davantage de résultats de dureté, mais elles sont également moins étudiées (et moins susceptibles d’être vraies). Le projet CONJEXITY, financé par le CER, résoudra les conjectures secondaires en les falsifiant ou en établissant leur équivalence avec une conjecture primaire.
Objectif
Fine-grained complexity theory identifies a small set of conjectures under which a large number of hardness results hold. The fast-growing list of such conditional hardness results already spans many diverse areas of computer science. Improved algorithms for some of the most central problems in these domains are deemed impossible unless one of the core conjectures turns out to be false, terminating decades-long quests for faster algorithms. Much research is going into closing the remaining gaps, addressing more domains, and achieving beyond-worst-case results.
But should these conjectures, that are the foundation of this entire theory, really be treated as laws of nature? In addition to three primary conjectures, the community has put forth about ten others. These ``secondary conjectures'' are often stronger variants of the primary conjectures, stating that the core problems remain hard despite introducing new assumptions on the input; they let us prove more hardness results but are also less extensively studied (and less likely to be true) compared to the original conjectures.
Stepping away from current research that is hustling towards achieving tight bounds for all important problems under such conjectures, this project aims to investigate the conjectures themselves. Our main objective is to resolve the secondary conjectures; either by falsifying them or by establishing their equivalence to a primary conjecture. Either of these two outcomes would be satisfying: Refuting a conjecture must involve disruptive algorithmic techniques, impacting numerous other problems. Unifying a secondary conjecture with an original (primary) conjecture reinforces the validity of the conjecture and all its implications, solidifying the very foundations of Fine-Grained Complexity. We believe that there is a pressing need for such an investigation of this rapidly growing theory.
Champ scientifique
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thème(s)
Régime de financement
ERC - Support for frontier research (ERC)Institution d’accueil
7610001 Rehovot
Israël