Algebra and Logic

NOVA Math > Research Groups > Algebra and Logic

About

The group focuses on various interconnected areas within Algebra and Logic. These areas include the investigation of structural and combinatorial properties of transformation semigroups, Young tableaux, crystals, automata algebra, semigroups, combinatorics on words, Ramsey theory, graph decomposition, and Turán functions. We also study linear and multilinear algebra, algebraic, differential, and non-commutative geometry, mathematical logic, ordered algebraic structures, and finite fields. Additionally, the group is interested in utilizing computational tools to develop experimental mathematics, aiming to gain fresh insights into the diverse realms of our research.

Team

Publications

Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories
2024, 32ND EACSL ANNUAL CONFERENCE ON COMPUTER SCIENCE LOGIC, CSL 2024, Antonelli,M;Dal Lago,U;Davoli,D;Oitavem,I;Pistone,P
ORIENTED TRANSFORMATIONS ON A FINITE CHAIN: ANOTHER DESCRIPTION (vol 38, pg 725, 2023)
2024, COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, Fernandes,VH
A complete solution for a nontrivial ruleset with entailing moves
2024, ELECTRONIC JOURNAL OF COMBINATORICS, Larsson,U;Nowakowski,RJ;Santos,CP
Timed Measurement Theory
2024, INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING, Skapinakis,E;Costa,JF
Cube-Based Isomorph-Free Finite Model Finding
2024, Frontiers in Artificial Intelligence and Applications - ECAI 2024, Chow,C;Janota,M;Araújo,J
On partial endomorphisms of a star graph
2024, QUAESTIONES MATHEMATICAE, Dimitrova,I;Fernandes,VH;Koppitz,J
SAT-Based Techniques for Lexicographically Smallest Finite Models
2024, THIRTY-EIGHTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE, VOL 38 NO 8, Janota,M;Chow,C;Araujo,J;Codish,M;Vojtechovsky,P
On monoids of endomorphisms of a cycle graph
2024, MATHEMATICA SLOVACA, Dimitrova,I;Fernandes,VH;Koppitz,J;Quinteiro,TM
On the cyclic inverse monoid on a finite set
2024, ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, Fernandes,VH
Endomorphisms of semigroups of monotone transformations
2024, JOURNAL OF ALGEBRA AND ITS APPLICATIONS, Li,DB;Fernandes,VH

Projects

Cohomology and extensions of inverse and restriction semigroups
No funding, Mykola Khrypchenko
Finitary incidence algebras and their generalized derivations
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazil), Mykola Khrypchenko
Generalized Derivations of Non-associative Algebras
FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Mykola Khrypchenko
Generalized Derivations of Incidence Algebras
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazil), Mykola Khrypchenko
Incidence Algebras
Fundação Araucária (Brazil), Mykola Khrypchenko
SemiComb - Semigroups: Conjugacy, Computation, Crystals and Combinatorics
FCT - Fundação para a Ciência e a Tecnologia, I.P., João Araújo, Tara Brough, Alan J. Cain, Ana Casimiro,...
Partial Actions, Restriction Semigroups and Monoidal Categories
No funding, Mykola Khrypchenko
Paul Bernays’ Philosophy of Mathematics
Swiss National Science Foundation (Switzerland), Reinhard Kahle
Hilbert's 24th Problem
FCT - Fundação para a Ciência e a Tecnologia, I.P., Reinhard Kahle, Alan James Cain, António José Mesquita...
"Research in Pairs" small grant
London Mathematical Society (United Kingdom), Alan J. Cain

Software

  •  
    • the kernel of a Theorem Prover interface: ProverX (under construction)
    • a package to find Forbidden Structure Conjectures: Forbidden Theorems
    • a package to find a base of identities for the variety of semigroups it generates: Semigroup Varieties
    • a package to translate proofs from Prover9 to other Automated Theorem Provers: Translator
    • a package to humanize proofs from Prover9: XPlain
    • to test if an identity is satisfied, given a set of semistandard tableaux