Semigroups, Automata and Languages

Crossconnection of Balanced Categories.

Speaker: 

P. G. Romeo

Date: 

Tuesday, 28 June, 2016 - 14:30

Venue: 

Room FC1.030, DMat-FCUP

A crossconnections between two balanced categories $\mathcal{C}$ and $\mathcal{D}$ is a local isomorphism $\Gamma : \mathcal{D}\to B*\mathcal{C}$ where $B*\mathcal{C}$ is the balanced dual of $\mathcal{C}$ such that the image of $\Gamma$ is total in $B*\mathcal{C}$. It is also such a crossconnection $\Gamma$ determines a concordant semigroup.

Categories in the structure theory of semigroups.

Speaker: 

A. R. Rajan

Date: 

Tuesday, 28 June, 2016 - 13:30

Venue: 

Room FC1.030, DMat-FCUP

Categories have been frequently used as a convenient tool in describing the structure of regular semigroups. Inductive groupoids of Schein for inverse semigroups, inductive groupoids of KSS Nambooripad for regular semigroups, categories of Rees groupoids of AR Rajan, normal categories of KSS Nambooripad, etc., are some of the instances. In this talk we consider normal categories associated with different classes of regular semigroups. Further the subcategories of inclusions, isomorphisms and retractions in normal categories will also be discussed.

Embedding Rationally Independent Languages into Maximal Ones.

Speaker: 

Stavros Konstantinidis

Date: 

Friday, 20 May, 2016 - 13:30

Venue: 

Room FC1.006, DMat-FCUP

We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We solve the problem by providing an embedding formula for the case where the code-related property is defined via a rational binary relation that is decreasing with respect to any fixed total order on the set of words. Our method works by iterating a max-min operator that has been used before for the embedding problem for properties defined by length-increasing-and-transitive binary relations.

Runtime Verification of Real-Time Systems: Logics and Architectures.

Speaker: 

David Pereira

Date: 

Friday, 13 May, 2016 - 13:30

Venue: 

Amphitheater 2, DCC-FCUP (FC6 029)

Real-time embedded systems are becoming more complex and open, making their development process extremely challenging and expensive, as well as much harder to verify and validate. Techniques like testing and simulation struggle to provide enough coverage of the system properties due increased number of reachable state of the system.

Introduction to temporal logics for verification.

Speaker: 

François Laroussinie

Date: 

Friday, 29 April, 2016 - 14:30

Venue: 

Amphitheater 2, DCC-FCUP

In this talk, we will see an overview of classical results about temporal logics (LTL, CTL, CTL*,…):  basic definitions, examples of properties, expressiveness, classical techniques for their decision procedures, complexity… We will also present several extensions of these logics and their use in the verification area.

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A Munn’s tree type representation for the bifree locally inverse semigroup.

Speaker: 

Luís Oliveira

Date: 

Friday, 15 April, 2016 - 13:30

Venue: 

Room FC1.005, DMat-FCUP

There are two traditional approaches to the free inverse semigroup. Scheiblich’s approach as pairs $(A,u)$ where $A$ is a “closed” set of group words and $u\in A$, and Munn’s approach where the elements of the free inverse semigroup are represented as birooted edge-labeled digraphs. Scheiblich’s approach has been generalized for the bifree locally inverse semigroup by Auinger. In this talk we generalize Munn’s approach. The straight bound between inverse semigroups and groups is now set in terms of locally inverse semigroups and completely simple semigroups.

Some results on generalised kernels of finite semigroups.

Speaker: 

Vicente Pérez-Calabuig

Date: 

Wednesday, 16 March, 2016 - 14:30

Venue: 

Room FC1.031, DMat-FCUP

The problem of computing kernels of finite semigroups goes back to the early seventies and became popular among semigroup theorists through the Rhodes Type II conjecture which proposed an algorithm to compute the kernel of a finite semigroup with respect to the class of all finite groups. Proofs of this conjecture were given in independent and deep works by Ash and Ribes and Zalesskiĭ, and the results of these authors that led to its proof have been extended in several directions.

The Trotter-Weil Hierarchy.

Speaker: 

Manfred Kufleitner

Date: 

Wednesday, 2 March, 2016 - 16:00

Venue: 

Room FC1.029, DMat-FCUP

The pseudovariety DA has a huge number of characterizations from very different areas - including algebra, formal languages and logic. The Trotter-Weil hierarchy is an infinite hierarchy of pseudovarieties inside DA.

In this talk, I will give a brief overview of the different characterizations of DA and their connection to the Trotter-Weil hierarchy.

C'era una volta in Porto... arrivederci Emanuele Rodaro!

Speaker: 

Francesco Matucci (State Univ. Campinas), Rogério Reis (Univ. Porto), Pedro Silva (Univ. Porto), Hossein Shahzamanian (Univ. Porto), Jorge Almeida (Univ. Porto), José Carlos Costa (Univ. Minho), Alfredo Costa (Univ. Coimbra), Emanuele Rodaro (Univ. Porto)

Date: 

Friday, 15 January, 2016 - 14:00

Venue: 

Room 0.29, Mathematics Department, Faculty of Sciences.

A mini-workshop dedicated to Emanuele Rodaro.

Program and abstracts may be found on: http://cmup.fc.up.pt/cmup/pvsilva/wer.pdf

An overview over conjugacy in semigroups.

Speaker: 

António Malheiro (Univ. NOVA of Lisbon / CMA)

Date: 

Friday, 4 December, 2015 - 14:15

Venue: 

Room FC1.004, DMat-FCUP

When generalizing a concept, it is sometimes tempting to think that there should be one correct, or even preferred, generalization.  Since semigroup theory is a vast subject, intersecting many areas of pure and applied mathematics, it is probably not reasonable to expect a one-size-fits-all notion of conjugacy suitable for all purposes.  Instead, we think that the goal of studying conjugacy in semigroups is to determine what different notions of conjugacy look like in various classes of semigroups, and how they interact with each other and with other mathematical concepts.

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