CORR
2008
Springer
13 years 4 months ago
2008
Springer
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations...
DAGSTUHL
2008
13 years 6 months ago
2008
: Let IIR be the set of closed and bounded intervals of real numbers. Arithmetic in IIR can be defined via the power set IPIR of real numbers. If divisors containing zero are exclu...
CCA
2005
Springer
13 years 6 months ago
2005
Springer
If one wishes to find out whether a computational problem over discrete data is solvable or how complex it is, the classical approach is to represent the discrete objects in quest...
TYPES
2000
Springer
13 years 8 months ago
2000
Springer
We describe a construction of the real numbers carried out in the Coq proof assistant. The basis is a set of axioms for the constructive real numbers as used in the FTA (Fundamenta...
MFCS
1993
Springer
13 years 8 months ago
1993
Springer
We present the different constructive definitions of real number that can be found in the literature. Using domain theory we analyse the notion of computability that is substant...
DATE
1999
IEEE
13 years 8 months ago
1999
IEEE
If real number calculations are implemented as circuits, only a limited preciseness can be obtained. Hence, formal verification can not be used to prove the equivalence between th...
STOC
2010
ACM
13 years 9 months ago
2010
ACM
We propose a new framework for discussing computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represente...
ICALP
2004
Springer
13 years 10 months ago
2004
Springer
Abstract We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: we p...
FOSSACS
2004
Springer
13 years 10 months ago
2004
Springer
Abstract. We show how to generate well-founded and stable term orderings based on polynomial interpretations over the real numbers. Monotonicity (another usual requirement in termi...
TPHOL
2005
IEEE
13 years 10 months ago
2005
IEEE
Wouldn’t it be nice to be able to conveniently use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem provin...