Topics of Interest
Since 1993 I work with the application of Topology, Algebra and Non-classical logics to the foundation of Interval Computations. Recently, I am enlarging my research to the application of interval matematics in some fields of computation; for example the extension of Fuzzy logics to Interval Fuzzy Logics (foundations and applications) and the application intervals and Non-classical logics to the field of Image Processing. If I would list the fields of computer science that I like to study I would give you the following list:
- Interval Mathematics;
- Logics;
- Domain Theory;
- Topology; and
- Semantics.
| Journals |
| 1. | SANTIAGO, R. H. N. ; BEDREGAL, Benjamin René Callejas ; ACIÓLY, B. M. . Formal Aspects of Correctness and Optimality of Interval Computations. Formal Aspects of Computing, v. 18, n. 2, p. 231-243, 2006. |
| 2. | SANTIAGO, R. H. N. ; MOREIRA, A. ; LOPES, K. . Implementing Local Intervals in CASL (To apperar). Electronic Notes in Theoretical Computer Science, 2006. |
| 3. | CARVALHO, Adriano X. ; SANTIAGO, R. H. N. . Interval Term Rewriting System: Toward a Formal Model for Interval Computations. Tendências Em Matemática Aplicada, v. 7, n.2, p. 249-258. 2006. |
| 4. | BEDREGAL, B. R. C. ; SANTIAGO, R. H. N. . Characterizing and Specifying Optimal and Correct Interval Functions (Submitted). Formal Aspects of Computing, 2006. |
| 5. | SANTIAGO, R. H. N. ; BEDREGAL, Benjamin René Callejas . Comparing Continuity of Interval Functions Based on Moore and Scott Topologies. Eletronic Journal on Mathematics of Computation, Recife-PE, v. 2, n. 1, p. 1-14, 2005. |
| Books |
| 1. | SANTIAGO, R. H. N. ; BEDREGAL, Benjamin René Callejas. Computability: The Boundaries of Computation (In Portuguese). 1. ed. São Carlos - SP: SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional, 2004. v. 500. 94 p. |
| 2006 - | Interval Computations: Foundations and Applications |
Description: Many problems and applications arise in the field of interval computations, some of them are: (a) the application of intervals as an element of uncertainty in the field of image processing and the extension of some programming languages with a high degree of portability to deal with interval processing . This project deals with those problems, it proposes the extension of the theory of mathematical morphology to deal with interval valued pixels and the extension of JAVA to interval computations. Situation: Running |
| 2002 - 2005 | Algebraic Specification and Scientific Computing |
Description: This project aims an integration between the fields of algebraic specifications and Scientific Computing. The goal is to enable the rigorous description of systems where the data which contains approximation errors could be verified and refined in a formal setting. The integration is done by the implementation in CASL of an interval library endowed with the notion of local equality. The project is applied in a specification of a system of this kind.
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| 2001 - 2004 | Formal Support to the Specification and Reutilization of Software |
Description: This project integrates the complementary knowledge of the brazilian and french teams in the fields of Rewritting Systems, Algebraic Specifications and Interval Computations. The project Ferus aims to contribute to the field of reutilization and specification of software. To do that, we apply formal technics developed by brazilian team, implementing a manager for libraryies of reusable components. We study the operations which are structuring constructors (which comes from the field of algebraic specification) and their application to the language ELAN (developed by the french team in the project PROTEO). We also aim the integration of these results to ELAN and to the environment of CASL. Finally we propose an extension for CASL in such a way that it could be able to support the specification of interval data.
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| MSc Students |
| 1. | José Frank Viana da Silva. Directed Rounding in Java. Start: 2006. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte. |
| PHD Students |
| 1. | Marcia Maria de Castro Cruz. The Mathematical Morphology of Interval Images: Foundations and Applications. Start: 2005. PhD Thesis (Electrical Engeneering) - Universidade Federal do Rio Grande do Norte. |
| Undergraduate Students |
| 1. | Thiago Medeiros Barros. A PHP library for IEEE-752 Floating-points. 2006. Scientific Initiation (Undergraduate in Computer Engineering) - Universidade Federal do Rio Grande do Norte, Sponsor: Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq |
Concluded Supervisions
| MSc Students |
| 1. | Adriano Xavier Carvalho. A Rewriting System for Intervals. 2005. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte. |
| 2. | Katiane Lopes. Extending CASL to Specify Systems with Comtinuous Data. 2004. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte, Sponsor: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES. |
| 3. | Maria José Lima dos Santos. Modelling PRAM-CRCW with Chu-Spaces. 2002. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte. |
| 4. | José Medeiros dos Santos. Toward a representation for Algebraic Equations: A Local Equational Logic. 2001. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte. |
| 5. | Marcia Maria de Castro Cruz. Equivalence and Consistency for Interval Functions. 2000. Master Thesis (Computer Science) - Universidade Federal do Rio Grande do Norte. |
| Undergraduate Students |
| 1. | Allan Rocha de Menezes. Specifying a Floating-point system in Isabele. 2006. Scientific Initiation. (Computer Science) - Universidade Federal do Rio Grande do Norte, Sponsor: Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq. |
| 2. | Kelly Patrícia da Silva. Automatic Proofs in Isabelle. 2004. Scientific Initiation. (Computer Engineering) - Universidade Federal do Rio Grande do Norte, Sponsor: Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq. |
| 3. | João Paulo de araújo Bezerra. Extending a CASL Library for Intervals. 2003. Scientific Initiation. (Computer Engineering) - Universidade Federal do Rio Grande do Norte. Sponsor: Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq. |
DIMAp means in Portuguese: "Departamento de Informática e Matemática Aplicada" (Department of Informatics and Applied Mathematics). It was created in 1985 and is located in one of the most beautiful brazilian littoral cities: Natal, in the state of Rio Grande do Norte (a state in the brazilian northeast region). In the last 20 years the department grew. In 1998, the brazilian council which coordinates the brazilian postgraduate courses, CAPES, approved the program for postgraduation in Computer Science called "Systems and Computation" which is basically composed by teachers of DIMAp. Since then, the department started a policy of supporting its teachers to enlarge their research contacts and knowledge exchange with a variety of important research groups in institutions like: LORIA-INRIA, Carnegie Mellon, Tours university (France), Technische Universität Berlin, National Spacial Institute of Research, PUC-Rio, Federal University of Pernambuco-UFPE, PETROBRÁS, etc). Some of these interactions gave origin to funded international cooperation projects. In 2006, some important brazilian events are being organized by DIMAp: Brazilian Symposium on Formal Methods (SBMF), Brazilian Symposium on Multimedia and the Web, Brazilian Symposium on Collaborative Systems, Brazilian Symposium on Human Factors on Computational Systems. In October 2006 we also organized the International Congress on Graph Transformation (ICGT).
So, this is a very little overview of our activities, for more information about DIMAp you can access www.dimap.ufrn.br (in Portuguese).
