Descrizione del progetto
Le congetture secondarie della complessità a grana fine: aggiornamento o archiviazione
La teoria della complessità computazionale è una branca della matematica che distingue tra soluzioni algoritmiche relativamente efficienti e soluzioni ingestibili. La teoria della complessità a grana fine cerca di migliorare la «risoluzione» di tali distinzioni, fornendo una determinazione quantitativa e potenzialmente una comprensione della complessità esatta dei problemi computazionalmente «difficili». Esistono tre congetture principali in base alle quali molti risultati di durezza sono validi. Esistono altre dieci congetture secondarie; possono essere varianti più forti, che ci permettono di dimostrare un maggior numero di risultati di durezza, ma sono anche meno studiate (e con meno probabilità di essere vere). Il progetto CONJEXITY, finanziato dal CER, risolverà le congetture secondarie falsificandole o stabilendo la loro equivalenza con una congettura primaria.
Obiettivo
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.
Campo scientifico
Programma(i)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Argomento(i)
Meccanismo di finanziamento
ERC - Support for frontier research (ERC)Istituzione ospitante
7610001 Rehovot
Israele