The project "Automata, Semigroups and Applications" aims to contribute to the development of the theories of automata and semigroups, and some of their applications. Besides connections between these areas of, say, Theoretical Informatics and Mathematics, they are also naturally connected with the theory of formal languages. On the other hand, the usage of sophisticated methods (as is the case of symbolic dynamics, representation theory, or geometric group theory) will also lead to the further exploration of natural connections with other branches of Mathematics.
The research team involves several experienced researchers, some with internationally recognized achievements, as well as five doctoral students, whose doctoral research is part of the project, and recent post-doctoral researchers. The team members are distributed by several R&D units, namely the "Centro de Matemática da Universidade do Porto" which is the Principal Research Unit, the "Laboratório de Inteligência Artificial e Ciência de Computadores", also from the University of Porto, the "Centro de Matemática" from the University of Minho, the "Centro de Matemática da Universidade de Coimbra", and the "Unidade de Investigação Matemática e Aplicações" from the University of Aveiro.
The project is organized in several tasks:
1. General theory of pseudovarieties
2. Free profinite semigroups and symbolic dynamics
3. Decidability through tameness
4. Pseudovarieties and representation theory
5. Combinatorial methods in group theory and semigroup theory
6. Bimachines: an algebraic approach to Turing machine computation
7. Descriptional complexity of regular languages
8. Computational tools
9. Practical algorithms in semigroups
10. Theory of existence varieties of regular semigroups