Complexity theory of real functions
Complexity theory of real functions
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Contents and abstracts of the electronic notes in Theoretical Computer Science Vol. 13
Theoretical Computer Science
Topological properties of real number representations
Theoretical Computer Science
A Foundation for Computable Analysis
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
The Appearance of Big Integers in Exact Real Arithmetic Based on Linear Fractional Transformations
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
| Hi-index | 5.23 |
This paper tries to classify the functions of type In → I (for some interval I ⊆ R) that can be exactly realized by a finite transducer. Such a class of functions strongly depends on the choice of real number representation. This paper considers only the so-called affine representations where numbers are represented by infinite compositions of affine contracting functions on I. Affine representations include the radix (e.g. decimal, signed binary) representations. The first result is that all piecewise affine functions of n variables with rational coefficients are computable by a finite transducer which uses the signed binary representation. The second and main result is that any function computable by a finite transducer using an affine representation is affine on any open connected subset of In on which it is continuously differentiable. This limitation theorem shows that the set of finitely computable functions is very restricted.