Search results for " complex"
showing 10 items of 3391 documents
MINIMALIST THEORY OF FICTION AND THE ICTHINKING® METHOD AS A BACKGROUND FOR NEW INSIGHTS TO AUTISM
2021
The standard approach to conceptual understanding in the case of autism uses the distinction of abstract versus concrete thinking. This approach has its benefits but fails to explain all features of language use. For example, some concepts change their meaning in different contexts in contrast to concepts that are more rigid in their uses, such as mathematical concepts. This idea has its background in Minimalist theory of fiction (MTF), a theory that considers ‘skills to use words’ essential for understanding fiction, contrasting with theories that require pretending or make believe to understand fiction. From this background, the theory of Integrative Complexity (IC), and the method animat…
Swarming Models for Facilitating Collaborative Decisions
2010
The paper highlights the computational power of swarming models (i.e., stigmergic mechanisms) to build collaborative support systems for complex cognitive tasks such as facilitation of group decision processes (GDP) in e-meetings. Unlike traditional approaches that minimize the cognitive complexity by incorporating the facilitation knowledge into the system, stigmergic coordination mechanisms minimize the complexity by providing the system with emergent functionalities that are shaped by the environment itself through the possibility to structure it in terms of high-level cognitive artefacts. This is illustrated by conducting a socio-simulation experiment for an envisioned collaborative sof…
Exceptional Configurations of Quantum Walks with Grover’s Coin
2016
We study search by quantum walk on a two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. We show what the most natural coin transformation -- Grover's diffusion transformation -- has a wide class of exceptional configurations of marked locations, for which the probability of finding any of the marked locations does not grow over time. This extends the class of known exceptional configurations; until now the only known such configuration was the "diagonal construction" by [AR08].
"Indexing structures for approximate string matching
2003
In this paper we give the first, to our knowledge, structures and corresponding algorithms for approximate indexing, by considering the Hamming distance, having the following properties. i) Their size is linear times a polylog of the size of the text on average. ii) For each pattern x, the time spent by our algorithms for finding the list occ(x) of all occurrences of a pattern x in the text, up to a certain distance, is proportional on average to |x| + |occ(x)|, under an additional but realistic hypothesis.
Quantum Query Complexity of Boolean Functions with Small On-Sets
2008
The main objective of this paper is to show that the quantum query complexity Q(f) of an N-bit Boolean function f is bounded by a function of a simple and natural parameter, i.e., M = |{x|f(x) = 1}| or the size of f's on-set. We prove that: (i) For $poly(N)\le M\le 2^{N^d}$ for some constant 0 < d < 1, the upper bound of Q(f) is $O(\sqrt{N\log M / \log N})$. This bound is tight, namely there is a Boolean function f such that $Q(f) = \Omega(\sqrt{N\log M / \log N})$. (ii) For the same range of M, the (also tight) lower bound of Q(f) is $\Omega(\sqrt{N})$. (iii) The average value of Q(f) is bounded from above and below by $Q(f) = O(\log M +\sqrt{N})$ and $Q(f) = \Omega (\log M/\log N+ \sqrt{N…
Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions
2007
For any AND-OR formula of size N, there exists a bounded-error N1/2+o(1)-time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in O(radicN) queries, which is optimal. It follows that the (2-o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy.
Circuit Lower Bounds via Ehrenfeucht-Fraisse Games
2006
In this paper we prove that the class of functions expressible by first order formulas with only two variables coincides with the class of functions computable by AC/sup 0/ circuits with a linear number of gates. We then investigate the feasibility of using Ehrenfeucht-Fraisse games to prove lower bounds for that class of circuits, as well as for general AC/sup 0/ circuits.
Span programs for functions with constant-sized 1-certificates
2012
Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the element distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph. We propose a solution for the same problems using span programs. The span program is a computational model equivalent to the quantum query algorithm in its strength, and yet very different in its outfit. We prove the power of our approach by designing a quantum algorithm for the triangle problem with query complexity O(n35/27) that is better than O(n13/10) of the best p…
Complexity of decision trees for boolean functions
2004
For every positive integer k we present an example of a Boolean function f/sub k/ of n = (/sub k//sup 2k/) + 2k variables, an optimal deterministic tree T/sub k/' for f/sub k/ of complexity 2k + 1 as well as a nondeterministic decision tree T/sub k/ computing f/sub k/. with complexity k + 2; thus of complexity about 1/2 of the optimal deterministic decision tree. Certain leaves of T/sub k/ are called priority leaves. For every input a /spl isin/ {0, 1}/sup n/ if any of the parallel computation reaches a priority leaves then its label is f/sub k/ (a). If the priority leaves are not reached at all then the label on any of the remaining leaves reached by the computation is f/sub k/. (a).
Enlarging the gap between quantum and classical query complexity of multifunctions
2013
Quantum computing aims to use quantum mechanical effects for the efficient performance of computational tasks. A popular research direction is enlarging the gap between classical and quantum algorithm complexity of the same computational problem. We present new results in quantum query algorithm design for multivalued functions that allow to achieve a large quantum versus classical complexity separation. To compute a basic finite multifunction in a quantum model only one query is enough while classically three queries are required. Then, we present two generalizations and a modification of the original algorithm, and obtain the following complexity gaps: Q UD (M′) ≤ N versus C UD (M′) ≥ 3N,…