Livros e artigos selecionados

N. C. A. da Costa and F. A. Dória, ``Undecidability and incompleteness in classical mechanics, Int. J. Theor. Physics vol. 30, pp. 1041-1073 (1991) Proves that chaos theory is undecidable and, if axiomatized within set theory, incomplete in the sense of Gödel.

N. C. A. da Costa and F. A. Dória, ``An undecidable Hopf bifurcation with an undecidable fixed point, Int. J. Theor. Physics vol. 33, pp. 1885-1903 (1994). Settles a question raised by V. I. Arnold in the list of problems drawn up at the 1974 American Mathematical Society Symposium on the Hilbert Problems: is the stability problem for stationary points algorithmically decidable?

I. Stewart, ``Deciding the undecidable, Nature vol. 352, pp. 664-665 (1991).

I. Stewart, From Here to Infinity, Oxford (1996). Comments on the undecidability proof for chaos theory.

J. Barrow, Impossibility - The Limits of Science and the Science of Limits, Oxford (1998). Describes the solution of Arnold's stability problem.

S. Smale, ``Problem 14: Lorenz attractor, in V. I. Arnold et al., Mathematics, Frontiers and Perspectives, pp. 285-286, AMS and IMU (2000). Summarizes the obstruction to decidability in chaos theory described by da Costa and Dória.

F. A. Dória and J. F. Costa, ``Special issue on hypercomputation, Applied Mathematics and Computation vol. 178 (2006).

N. C. A. da Costa and F. A. Dória, ``Consequences of an exotic formulation for P = NP, Applied Mathematics and Computation vol. 145, pp. 655-665 (2003) and vol. 172, pp. 1364-1367 (2006). The criticisms to the da Costa-Dória approach appear in the references in those papers.

N. C. A. da Costa, F. A. Dória and E. Bir, ``On the metamathematics of the P vs. NP question, to be published in Applied Mathematics and Computation (2007). Reviews the evidence for a conjectured consistency of P = NP with some strong axiomatic theory.

A. Syropoulos, Hypercomputation: Computing Beyond the Church-Turing Barrier, Springer (2008). Describes the contribution to hypercomputation theories by da Costa and Dória, and sketches their contribution to the P = NP problem.