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AML
2008
124views more  AML 2008»
13 years 7 months ago
The elementary computable functions over the real numbers: applying two new techniques
The basic motivation behind this work is to tie together various computational complexity classes, whether over different domains such as the naturals or the reals, or whether def...
Manuel Lameiras Campagnolo, Kerry Ojakian
DAGSTUHL
2008
13 years 9 months ago
Real Algebraic Numbers: Complexity Analysis and Experimentation
Abstract. We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree d, with integer coefficients of bit size , using S...
Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsig...
ITA
2007
104views Communications» more  ITA 2007»
13 years 7 months ago
Automata, Borel functions and real numbers in Pisot base
This note is about functions f : Aω → Bω whose graph is recognized by a B¨uchi finite automaton on the product alphabet A × B. These functions are Baire class 2 in the Bair...
Benoit Cagnard, Pierre Simonnet
CADE
2009
Springer
14 years 8 months ago
A Generalization of Semenov's Theorem to Automata over Real Numbers
Abstract This work studies the properties of finite automata recognizing vectors with real components, encoded positionally in a given integer numeration base. Such automata are us...
Bernard Boigelot, Jérôme Leroux, Juli...
ARITH
2009
IEEE
14 years 2 months ago
A Dual-Purpose Real/Complex Logarithmic Number System ALU
—The real Logarithmic Number System (LNS) allows fast and inexpensive multiplication and division but more expensive addition and subtraction as precision increases. Recent advan...
Mark G. Arnold, Sylvain Collange