Curriculum Vitae. Bruno Loff. Born on December the 2nd, 1984, in Lisbon, Portugal. Rua Vitorino Nemésio, n o 8, 4 o Esq , Lisboa, Portugal

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1 Curriculum Vitae Bruno Loff Born on December the 2nd, 1984, in Lisbon, Portugal Rua Vitorino Nemésio, n o 8, 4 o Esq , Lisboa, Portugal (+351) bruno.loff@gmail.com July 3,

2 Summary statement Bruno Loff enrolled in Information Systems and Computer Engineering in 2001, discovering only in his third year a profound interest in theoretical computer science, especially computability and computational complexity, and the education of Mathematics. He chose to finish this graduation, while simultaneously attending all Mathematics courses in the curriculum and a few extra-curricular courses, consistently obtaining top-grades in his fields of interest. Since the fourth year of his graduation he has been working in theoretical computer science. He discovered new results both alone and in collaboration with other researchers which were publicly published and presented in international journals and conferences. He is currently finishing his graduation under the most excellent and appreciated orientation of Professor José Félix Costa, with whom he has co-authored most of his work. Research Interests Structural Computational Complexity (main interest), Computability, History and Philosophy of Science (particularly Mathematics and Computation)... Academic degrees 2001/ /07 Instituto Superior Técnico, Technical University of Lisbon, Information Systems and Computer Engineering, major in theory of computation. Graduation average is 16 so far. Grades for favourite courses are: Computability: 20, Computational Complexity: 20, Neurocomputation: 20, Lambda Calculus: 19, Mathematical Logic: 19, Algorithms: 17, Computational Logic: 18, Functional Analysis: 13 É enviado em anexo um certificado de inscrição no regime transitório. expected date This was a course in Functional Analysis that Bruno took for the sake of it, and without attending the previous courses Introduction to Topology and Functional Analysis, and Topology which introduced the subject to Mathematics students. Also missed where the specialised courses in Linear Algebra, Algebra I and II, Measure and Integration, etc, which were all part of the curriculum of every one of his six or seven colleagues who also took the course that semester. Bruno got the third best grade. 2

3 Affiliation Member of Centro de Matemática e Aplicações Fundamentais (CMAF) of the University of Lisbon Language Skills Portuguese (native language), English (Scored A in the Certificate of Proficiency in English (CPE) of the University of Cambridge), Spanish (listening, reading and speaking), French (reading only). 3

4 Peer-reviewed articles 2007 Bruno Loff, and José Félix Costa. Five views of hypercomputation. Accepted for publication in the International Journal of Unconventional Computing. Abstract. We overview different approaches to the study of hypercomputation and other investigations on the plausibility of the physical Church Turing thesis. We propose five thesis to classify investigation in this area José Félix Costa, Bruno Loff, and Jerzy Mycka. The new promise of analog computation. Appears in S. B. Cooper, B. Löwe, and A. Sorbi (eds.), Lecture Notes in Computer Science 4497: , Springer, Abstract. We show that, using our more or less established framework of inductive definition of real-valued functions (work started by Cristopher Moore in 1996) together with ideas and concepts of standard computability we can prove theorems of Analysis. Then we will consider our ideas as a bridging tool between the standard Theory of Computability (and Complexity) on one side and Mathematical Analysis on the other, making real recursive functions a possible branch of Descriptive Set Theory. What follows is an Extended Abstract directed to a large audience of CiE 2007, Special Session on Logic and New Paradigms of Computability Bruno Loff. A functional characterization of the analytical hierarchy. Appears in S. B. Cooper, B. Löwe, and A. Sorbi (eds.), Computation and Logic in the Real World (local proceedings of CiE 07 ). Abstract. We study an inductive class of vector functions over the reals, defined from a set of basic functions by composition, solving of first order differential equations and the taking of infinite limits. We show that we obtain exactly the class of vector functions for which z = f( x) is a predicate in the analytical hierarchy. We then prove an analogue of Post s theorem for the analytical hierarchy Bruno Loff, José Félix Costa, and Jerzy Mycka. Computability on reals, infinite limits and differential equations. Accepted for publication in Journal of Applied Mathematics and Computation. 4

5 Abstract. We study a countable class of real-valued functions inductively defined from a basic set of trivial functions by composition, solving first-order differential equations and the taking of infinite limits. This class is the analytical counterpart of Kleene s partial recursive functions. By counting the number of nested limits required to define a function, this class can be stratified by a potentially infinite hierarchy a hierarchy of infinite limits. In the first meaningful level of the hierarchy we have the extensions of classical primitive recursive functions. In the next level we find partial recursive functions, and in the following level we find the solution to the halting problem. We use methods from numerical analysis to show that the hierarchy does not collapse, concluding that the taking of infinite limits can always produce new functions from functions in the previous levels of the hierarchy. Reports 2007 Bruno Loff. On two variants of the Church Turing thesis. Abstract. We study the Church Turing thesis, focusing on two specific variants called the physical Church Turing thesis and the simulation thesis. We outline how the study of these two thesis should proceed, identifying the essentials stages of investigation. We overview work on these thesis, distinguishing these different stages. Presentations in conferences and workshops José Félix Costa, Bruno Loff, and Jerzy Mycka. The new promise of analog computation. Invited paper, presented in Computability in Europe 2007: Computation and Logic in the Real World. Bruno Loff. A functional characterization of the analytical hierarchy. Presented in Computability in Europe 2007: Computation and Logic in the Real World. Bruno Loff. A functional characterization of the analytical hierarchy. Workshop in Statistics, Mathematics and Computation, Poster by Bruno Loff, José Félix Costa, and J. Mycka. The hierarchy of real recursive functions. Unconventional Computation

6 Poster by Bruno Loff. Real recursive functions and the analytical hierarchy. Unconventional Computation Seminar lessons Using physical measurements as an oracle for computation. Mathematical Logic Seminar, June Turing degrees in the real world investigation and discussion of the physical Church Turing thesis and hypercomputation. Mathematical Logic Seminar, January A functional characterization of the analytical hierarchy. Mathematical Logic Seminar. November Gödel s first incompleteness theorem. Diagonal Seminar. September Computability on reals, differential equations and infinite limits. Mathematical Logic Seminar. May