1,984,693 research outputs found
The Frobenius complexity of Hibi rings
We study the Frobenius complexity of Hibi rings over fields of characteristic
. In particular, for a certain class of Hibi rings (which we call
-level), we compute the limit of the Frobenius complexity as .Comment: minor edits, to appear in Journal of Pure and Applied Algebr
On Complexity for Higher Derivative Gravities
Using "complexity=action" proposal we study complexity growth of certain
gravitational theories containing higher derivative terms. These include
critical gravity in diverse dimensions. One observes that the complexity growth
for neutral black holes saturates the proposed bound when the results are
written in terms of physical quantities of the model. We will also study
effects of shock wave to the complexity growth where we find that the presence
of massive spin-2 mode slows down the rate of growth.Comment: 18 pages, 3 figures, journal versio
Faster Algorithms for Rectangular Matrix Multiplication
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha}
matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic
operations. In this paper we show that \alpha>0.30298, which improves the
previous record \alpha>0.29462 by Coppersmith (Journal of Complexity, 1997).
More generally, we construct a new algorithm for multiplying an n x n^k matrix
by an n^k x n matrix, for any value k\neq 1. The complexity of this algorithm
is better than all known algorithms for rectangular matrix multiplication. In
the case of square matrix multiplication (i.e., for k=1), we recover exactly
the complexity of the algorithm by Coppersmith and Winograd (Journal of
Symbolic Computation, 1990).
These new upper bounds can be used to improve the time complexity of several
known algorithms that rely on rectangular matrix multiplication. For example,
we directly obtain a O(n^{2.5302})-time algorithm for the all-pairs shortest
paths problem over directed graphs with small integer weights, improving over
the O(n^{2.575})-time algorithm by Zwick (JACM 2002), and also improve the time
complexity of sparse square matrix multiplication.Comment: 37 pages; v2: some additions in the acknowledgment
Average-Case Quantum Query Complexity
We compare classical and quantum query complexities of total Boolean
functions. It is known that for worst-case complexity, the gap between quantum
and classical can be at most polynomial. We show that for average-case
complexity under the uniform distribution, quantum algorithms can be
exponentially faster than classical algorithms. Under non-uniform distributions
the gap can even be super-exponential. We also prove some general bounds for
average-case complexity and show that the average-case quantum complexity of
MAJORITY under the uniform distribution is nearly quadratically better than the
classical complexity.Comment: 14 pages, LaTeX. Some parts rewritten. This version to appear in the
Journal of Physics
Myths of Complexity
The following article takes up a dialogue that was initiated in the first issue of Design Ecologies, evolving in relation to questions of design within a context of concepts of complexity. As the first part of the article shows, this process of taking up a dialogue – through reading and writing – can be considered a question of design. This is elaborated alongside de Certeau’s concepts of ‘tactics’ and ‘strategies’. Further, in relation to questions emerging from the previous issue of the Design Ecologies journal, the article addresses the notion of complexity through the conceptual lens of poiesis. It leads complexity to the borders of language
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