873 research outputs found
Quantum Bounded Query Complexity
We combine the classical notions and techniques for bounded query classes
with those developed in quantum computing. We give strong evidence that quantum
queries to an oracle in the class NP does indeed reduce the query complexity of
decision problems. Under traditional complexity assumptions, we obtain an
exponential speedup between the quantum and the classical query complexity of
function classes.
For decision problems and function classes we obtain the following results: o
P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in
EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is
included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE
or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one
complete for PP have the property that FP_||^A is included in FEQP^A[1]. In
general we prove that for any set A there is a set X such that FP^A is included
in FEQP^X[1], establishing that no set is superterse in the quantum setting.Comment: 11 pages LaTeX2e, no figures, accepted for CoCo'9
Combinatorics of lattice paths with and without spikes
We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.Comment: Latex. 25 page
Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]
Roger Apery's seminal method for proving irrationality is "turned on its
head" and taught to computers, enabling a one second redux of the original
proof of zeta(3), and many new irrationality proofs of many new constants,
alas, none of them is both famous and not-yet-proved-irrational.Comment: 16 pages. Exclusively published in the Personal Journal of Shalosh B.
Ekhad and Doron Zeilberger, May 2014, and this arxiv.org. Accompanied my
Maple package NesApery, available from
http://www.math.rutgers.edu/~zeilberg/tokhniot/NesAper
Fast Reduction of Bivariate Polynomials with Respect to Sufficiently Regular Gröbner Bases
International audienc
- …