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Contenido archivado el 2024-06-18

Understanding the Hardness of Theorem Proving

Objetivo

This project aims to explore the fundamental question in computer science and mathematics regarding what computational problems can feasibly be solved on a computer. More specifically, we want to study algorithms for proving logic formulas as well as impossibility results for this problem.

Proving formulas in propositional logic is a problem of immense importance both theoretically and practically. On the one hand, this computational task is believed to be intractable in general, and deciding whether this is so is one of the famous million dollar Millennium Problems (the P vs NP problem). On the other hand, today automated theorem provers, or so-called SAT solvers, are routinely used to solve large-scale real-world problem instances with even millions of variables. This contrasts to that there are also known small example formulas with just hundreds of variables that cause even state-of-the-art SAT solvers to stumble.

The main objectives of our project are as follows:

(1) Understand what makes formulas hard or easy in practice by building and studying better theoretical models of the proof systems underlying SAT solvers, and testing the predictions of these models against empirical data.

(2) Gain theoretical insights into other crucial issues in SAT solving such as memory management and parallelization.

(3) Explore the possibility of basing SAT solvers on stronger proof systems than are currently being used.

(4) Clarify the theoretical limitations of such enhanced SAT solvers by studying the corresponding proof systems, which are currently poorly understood.

We see great opportunities for fruitful interplay between the fields of proof complexity and SAT solving in this area, as well as between theoretical results and practical implementations. We believe that resolving the questions posed by this project could potentially have a major impact in theoretical computer science, and in the longer term in more applied areas of computer science and mathematics.

Convocatoria de propuestas

ERC-2011-StG_20101014
Consulte otros proyectos de esta convocatoria

Régimen de financiación

ERC-SG - ERC Starting Grant

Institución de acogida

KUNGLIGA TEKNISKA HOEGSKOLAN
Aportación de la UE
€ 1 460 000,00
Dirección
BRINELLVAGEN 8
100 44 Stockholm
Suecia

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Región
Östra Sverige Stockholm Stockholms län
Tipo de actividad
Higher or Secondary Education Establishments
Contacto administrativo
Harriett Johansson (Ms.)
Investigador principal
Karl Jakob Nordström (Dr.)
Enlaces
Coste total
Sin datos

Beneficiarios (1)