Abstract Geometrical Computation and Computable Analysis

Geometrical Computation and Computable Analysis J´erˆome Durand-Lose⋆ Laboratoire d’Informatique Fondamentale d’Orl´eans, Universit´e d’Orl´eans, B.P. 6759, F-45067 ORL´EANS Cedex 2, France Extended Signal machines are proven able to compute any computable function in the understanding of recursive/computable analysis (CA), here type-2 Turing machines (T2-TM) with signed binary encoding. This relies on an intermediate representation of any real number as an integer (in signed binary) plus an exact value in (−1, 1) which allows to have only finitely many signals present outside of the computation. Extracting a (signed) bit, improving the precision by one bit and iterating the T2-TM only involve standard signal machines. For exact CA-computations, T2-TM have to deal with an infinite entry and to run through infinitely many iterations to produce an infinite output. This infinite duration can be provided by constructions emulating the black hole model of computation on...

• Type: Conference
• Year: 2009
• Where: UC
• Authors: Jérôme Durand-Lose
• Keywords: Applied Computing, Extended Signal Machine, Geometrical Computation, Signal Machine, UC 2009