Descripción del proyecto
Conjeturas secundarias de la complejidad de grano fino: mejora o refutación
La teoría de la complejidad computacional es una rama de las matemáticas que distingue entre soluciones algorítmicas relativamente eficientes y aquellas que son inabordables. La teoría de la complejidad de grano fino busca mejorar la «resolución» de tales distinciones, al ofrecer una determinación cuantitativa y, quizás, una idea de la complejidad exacta de los problemas computacionalmente «complejos». Existen tres conjeturas principales en las que se basan muchos resultados de dureza. Hay otras diez conjeturas secundarias; pueden ser variantes más fuertes, que pueden permitir probar más resultados de dureza, pero que se han estudiado bastante menos (y es menos probable que sean ciertas). En el proyecto CONJEXITY, financiado por el Consejo Europeo de Investigación, se resolverán las conjeturas secundarias refutándolas o estableciendo su equivalencia con una conjetura primaria.
Objetivo
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.
Ámbito científico
Programa(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régimen de financiación
ERC - Support for frontier research (ERC)Institución de acogida
7610001 Rehovot
Israel