We present the role that spectral methods play in the development of the most impressive quantum algorithms, such as the polynomial time number factoring algorithm by Shor. While ...
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, ...
We present an exact algorithm for the computation of the moments of a region bounded by a curve represented in a scaling function or wavelet basis. Using Green's theorem, we ...
We describe an approach to using one logic to reason about specifications written in a second logic. One level of logic, called the "reasoning logic", is used to state th...
This paper presents a new functional computation model for developing a class of two-variable Lambda-Boolean functions, and describes the properties of the duality principle on th...