Paulo Blauth Menezes

A Categorical Approach to NP-Hard Optimization Problems

Aiming at developing a theoretical framework for the formal study of NP-hard optimization problems, which is built on precise mathematical foundations, we have focused on structural properties of optimization problems related to approximative issue. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, in this work we present a categorical approach to cope with some questions originally studied within Computational Complexity Theory. After defining the polynomial time soluble optimization problems category OPTS and the optimization problems category OPT, a comparison mechanism between them and an approximation system to each optimization problem have been introduced, following the basic idea of categorical shape theory. In this direction, we consider new insights and a deeper understanding of some basic questions inside the Structural Complexity field, by an universal language.

Hyper-Automation System Applied to Geometry Demonstration Environment

This paper describes the conception and implementation of a learning system on Euclidean Geometry demonstrations and its knowledge base. We use the formalism of finite automata with output to represent and ordain the statements that constitute a geometric demonstration in the knowledge base. The system is built on the MOSCA learning protocol, based on learning with the assistance of examples and interaction among five agents (Mestre, Oraculo, Sonda, Cliente and Aprendiz) involved in the learning process. We briefly revise the Hyper-Automaton concept as a structural model for hypertext and its use as the basis for the central core of the agents in a learning system is analyzed.

Mapping Nautilus language into java: Towards a specification and programming environment for distributed systems

This paper describes some of the features of Nautilus specification/ programming language that make it interesting to develop complex systems and then explains how to map a Nautilus construction into Java constructions. The Nautilus constructions presented are: actions (including nondeterminism and intra-action concurrency), aggregations and refinements.

Massive Open Online Courses and Monoids

Massive open online courses (MOOC) allows for distributed long-distance learning for extremely large student enrollment. Nowadays most universities throughout the world have their courses online. Web portals such as Coursera or edX join together courses from many of them. Even though there are many platforms to support the development of MOOC, such as Moodle or XBlock, it does not seem to be the case that there are many languages to help course descriptions. Moreover, we would like to allow the description of different paths to teach and learn a given subject. We propose Learn, a declarative language for course descriptions. The contribution of this paper is manyfold: (i) we exemplify Learn descriptions, (ii) formalize the meaning of Learn descriptions and teaching strategies, that allows for different teaching paths, and (iii) discuss the implementation of a toolkit to specify, analyze and generate a course in a MOOC platform from Learn descriptions.

Nautilus, a Concurrent Diagrammatic Specification and Programming Language

Nautilus is a high-level specification and programming language having abstraction mechanisms not commonly found in other programming languages inspired by its semantic domain (a categorial model named Nonsequential Automata). It constitutes an elegant solution for concurrency and non-determinism as well as for synchronization of concurrent systems. The role as specification language highlights the diagrammatic syntax (it was originally text based).The diagrammatic syntax for Nautilus allows complete programs to be written using symbols and graphical diagrams. The graphical notation was elaborated in order to be able to express all the structures in the language, yet trying to improve the visualization of written programs. A brief comparison with UML is included. To support Nautilus as a programming language, a mapping to Java is constructed, setting the basis for an execution environment of Nautilus specifications.

O Ambiente de Autoria do AdaptHA

AdaptHA e um ambiente de ensino adaptativo na Web baseado no modelo Hyper-Automaton que objetiva proporcionar ao aluno uma experiencia de aprendizagem individualizada ao apresentar o material instrucional adaptado com base em seu nivel de conhecimento e preferencias. Este artigo objetiva apresentar o ambiente de autoria do AdaptHA, que reune um rico conjunto de ferramentas que visa facilitar as tarefas de autoria do professor .

Composing transitions into transactions in UML diagrams

When modeling concurrent or parallel systems, we must be aware that basic activities of each system may be constituted by smaller activities, i.e. transitions may be conceptually refined into transactions. Nevertheless, the Unified Modeling Language seems to lack compositional constructs for defining atomic actions/activities/operations. We discuss proper extensions for UML behavioral diagrams that are able to cope with the concept of transaction. Transactions are formally defined through a special morphism between automata in a semantic domain called Nonsequential Automata.

Approximation problems categories

In this paper we continue along the same line of research started in earlier works, towards to providing a categorical view of structural complexity to optimization problems. The main aim is to provide a universal language for supporting formalisms to specify the hierarchy approximation system for an abstract NP-hard optimization problem. Categorical shape theory provides the mathematical framework to deal with approximation, enabling comparison of objects of interest and of models. In this context, tractable optimization problems are considered as a class of “models” or “prototypes” within a larger class of objects of interest – the intractable optimization problems class. Standard categorial constructions like universal objects, functors and adjunctions allow to formalize an approximation hierarchy system to optimization problems, besides characterizing NP-hard optimization problems as concrete universal objects.

Computation of partial automata through span composition

In this paper a way to have structures with partiality in its internal structure in a categorical approach is presented and, with this, a category of partial graphs

Computational simulation of categorical constructions

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