NEAT
Financiado
Non-linear Existential Arithmetic Theories
Arithmetic theories are logical theories about systems of numbers that found important applications in several areas of computer science. For instance, those theories have a fundamental role in Satisfiability Modulo Theory (SMT),...
Arithmetic theories are logical theories about systems of numbers that found important applications in several areas of computer science. For instance, those theories have a fundamental role in Satisfiability Modulo Theory (SMT), abstract interpretation and symbolic execution, the three most prominent algorithmic techniques to type check or bug test programs against rich specification languages. In optimisation, Integer Linear Programming offers a general framework to model many scheduling, planning and network problems using linear integer arithmetic. In Theoretical Computer Science, several computational problems stemming from formal logic and automata theory require arithmetic theories procedures to be solved.
Arithmetic theories are simple to describe, but their algorithms are based on profound mathematical theories. The goal of this proposal is to achieve a major advance in algorithms for decision and optimisation problems of existential arithmetic theories featuring the non-linear operators of exponentiation and divisibility. We choose to focus on these two operators for both theoretical and practical reasons. On the theory side, whereas multiplication often causes decidability issues (see e.g. the undecidability of Hilbert’s 10th problem), exponentiation and divisibility are much more algorithmically robust. On the practical side, these two non-linear operators have recently found several applications in the aforementioned areas of computer science.
To achieve our goal, our methodology combines several areas of mathematics and theoretical computer science: automata theory, combinatorics, non-convex geometry, model theory and number theory. While the content of the proposal is foundational in nature, the long-term goal is for algorithms developed during the project to serve as a basis to expand the capabilities of SMT solvers, static analysers and optimization tools, making them able to handle very expressive languages of arithmetic.
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Duración del proyecto: 40 meses
Fecha Inicio: 2024-04-03
Fecha Fin: 2027-08-31
Fecha Fin: 2027-08-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2024-04-03
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2023-PF-01-01:
MSCA Postdoctoral Fellowships 2023
Cerrada
hace 1 año
Presupuesto
El presupuesto total del proyecto asciende a
181K€
Líder del proyecto
IMDEA SOFTWARE INSTITUTE
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
650K
Perfil tecnológico
TRL
4-5
650K