Complexity theory of real functions
Complexity theory of real functions
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Abstract Geometrical Computation 1: Embedding Black Hole Computations with Rational Numbers
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Abstract Geometrical Computation and the Linear Blum, Shub and Smale Model
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
(Short) Survey of Real Hypercomputation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Abstract geometrical computation 3: black holes for classical and analog computing
Natural Computing: an international journal
Geometrical accumulations and computably enumerable real numbers
UC'11 Proceedings of the 10th international conference on Unconventional computation
Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Abstract geometrical computation 7: geometrical accumulations and computably enumerable real numbers
Natural Computing: an international journal
Hi-index | 0.00 |
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 an extended signal machine. Extracting/encoding an infinite sequence of bits is achieved as the limit of the approximation process with a careful handling of accumulations and singularities.