Project description
Algorithms for non-linear existential arithmetic theories
In computer science, arithmetic theories are crucial for addressing complex problems, particularly in Satisfiability Modulo Theory (SMT) and static analysis. However, these theories often involve algorithms rooted in mathematical principles. Issues such as undecidability in problems involving multiplication complicate the development of effective solutions. As a result, there is a pressing need to enhance algorithms that can handle non-linear arithmetic operations. Supported by the Marie Skłodowska-Curie Actions programme, the NEAT project will focus on the non-linear operators of exponentiation and divisibility. By leveraging a multidisciplinary approach that includes automata theory, combinatorics, and number theory, NEAT seeks to develop robust algorithms that can expand the capabilities of SMT solvers and optimisation tools.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2023-PF-01
See all projects funded under this callCoordinator
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
28223 Pozuelo De Alarcon
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.