A numerical semigroup $S$ is a submonoid of $(\mathbb N,+)$ with finite complement in $\mathbb N$. Integers not in $S$ are called gaps of $S$. The largest gap is known as the Frobenius number of $S$, $F(S)$. A gap $x$ is a hole, if $F(S)-x$ is also a gap.
...
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. In joint work with Bettina Eick I investigate a similar approach for the study of finite nilpotent semigroups.
...
Jorge Sousa Pinto (Departamento de Informática, Escola de Engenharia, Universidade do Minho
Date:
Wednesday, 30 November, 2011 (All day)
Venue:
S2, DCC-FCUP
A mechanism for generating verification conditions (VCs) for the iteration-free fragment of an imperative language is fundamental in any deductive program verification system. In this paper we revisit symbolic execution, weakest preconditions, and bounded model checking as VC-generation...
(Join work with Pedro Silva) We show that the word problem for an amalgam [S1, S2; U, ω1, ω2] of inverse semigroups may be undecidable even if we assume S1 and S2 (and therefore U) to have finite R-classes and ω1, ω2 to be computable functions, interrupting a series of...
Finite automata became over the years the standard representation of finitely generated subgroups $H$ of a free group $F_A$. The Stallings construction constitutes a simple and efficient algorithm for building an automaton $S(H)$ which can be used for solving the membership problem of $H$ in $F_A...
Partition monoids and algebras arise in representation theory in the context of Schur-Weyl duality in symmetric groups. They are also interesting from a semigroup theoretic point of view as they contain the full transformation semigroups as well as the symmetric (and dual symmetric) inverse...
Given a free group $F_r$ on $A = \{ a_1, \ldots, a_r\}$ and an automorphism $\varphi$ of $F_r$, we can consider the norm $||\varphi|| = |a_1\varphi| + \ldots + |a_r\varphi|$. How big can be $||\varphi^{-1}||$ relatively to $||\varphi||$? More precisely, this talk concerns the complexity of the...
The Karoubi envelope of a semigroup is a small category which plays a distinguished role in finite semigroup theory thanks to the Delay theorem of Tilson. In this talk, an application to the classification of symbolic dynamical systems is presented: up to natural equivalence, the Karoubi envelope...