Search results for "computational complexity"
showing 10 items of 249 documents
Positive Versions of Polynomial Time
1998
Abstract We show that restricting a number of characterizations of the complexity class P to be positive (in natural ways) results in the same class of (monotone) problems, which we denote by posP . By a well-known result of Razborov, posP is a proper subclass of the class of monotone problems in P . We exhibit complete problems for posP via weak logical reductions, as we do for other logically defined classes of problems. Our work is a continuation of research undertaken by Grigni and Sipser, and subsequently Stewart; indeed, we introduce the notion of a positive deterministic Turing machine and consequently solve a problem posed by Grigni and Sipser.
A local complexity based combination method for decision forests trained with high-dimensional data
2012
Accurate machine learning with high-dimensional data is affected by phenomena known as the “curse” of dimensionality. One of the main strategies explored in the last decade to deal with this problem is the use of multi-classifier systems. Several of such approaches are inspired by the Random Subspace Method for the construction of decision forests. Furthermore, other studies rely on estimations of the individual classifiers' competence, to enhance the combination in the multi-classifier and improve the accuracy. We propose a competence estimate which is based on local complexity measurements, to perform a weighted average combination of the decision forest. Experimental results show how thi…
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].
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.
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).
On the decision problem for the guarded fragment with transitivity
2002
The guarded fragment with transitive guards, [GF+TG], is an extension of GF in which certain relations are required to be transitive, transitive predicate letters appear only in guards of the quantifiers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. This answers the question posed in (Ganzinger et al., 1999). Moreover, we show that the problem is 2EXPTIME-complete. This result is optimal since the satisfiability problem for GF is 2EXPTIME-complete (Gradel, 1999). We also show that the satisfiability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satisfiability pr…
On the Finite Satisfiability Problem for the Guarded Fragment with Transitivity
2005
We study the finite satisfiability problem for the guarded fragment with transitivity. We prove that in case of one transitive predicate the problem is decidable and its complexity is the same as the general satisfiability problem, i.e. 2Exptime-complete. We also show that finite models for sentences of GF with more transitive predicate letters used only in guards have essentially different properties than infinite ones.
Quantum Query Complexity for Some Graph Problems
2004
The paper [4] by H. Buhrman and R. de Wolf contains an impressive survey of solved and open problems in quantum query complexity, including many graph problems. We use recent results by A.Ambainis [1] to prove higher lower bounds for some of these problems. Some of our new lower bounds do not close the gap between the best upper and lower bounds. We prove in these cases that it is impossible to provide a better application of Ambainis’ technique for these problems.
Quantum Identification of Boolean Oracles
2004
The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…
On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets
2000
We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem for analog Hopfield nets is NP-hard and provide a polynomial time approximation algorithm for this p…