One of the central problems in quantum mechanics is to determine the ground-state properties of a system of electrons interacting through the Coulomb potential. Since its introduction(1,2), density functional theory h...
详细信息
One of the central problems in quantum mechanics is to determine the ground-state properties of a system of electrons interacting through the Coulomb potential. Since its introduction(1,2), density functional theory has become the most widely used and successful method for simulating systems of interacting electrons. Here, we show that the field of computational complexity imposes fundamental limitations on density functional theory. In particular, if the associated 'universal functional' could be found efficiently, this would imply that any problem in the computational complexity class Quantum Merlin Arthur could be solved efficiently. Quantum Merlin Arthur is the quantum version of the class NP and thus any problem in NP could be solved in polynomial time. This is considered highly unlikely. Our result follows from the fact that finding the ground-state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, but, given the universal functional, it can be computed efficiently using density functional theory. This work illustrates how the field of quantum computing could be useful even if quantum computers were never built.
Forty Thieves is a solitaire game with two 52-card decks. The object is to move all cards from ten tableau piles of four cards to eight foundations. Each foundation is built up by suit from ace to king of the same sui...
详细信息
Forty Thieves is a solitaire game with two 52-card decks. The object is to move all cards from ten tableau piles of four cards to eight foundations. Each foundation is built up by suit from ace to king of the same suit, and each tableau pile is built down by suit. You may move the top card from any tableau pile to a tableau or foundation pile, and from the stock to a foundation pile. We prove that the generalized version of Forty Thieves is NP-complete.
We investigate I he computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precis...
详细信息
We investigate I he computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense. (C) 2009 Elsevier B.V. All rights reserved.
It is known that the problem of maximizing the sum degrees of freedom (DoF) for an arbitrary MIMO network without symbol extension is NP-hard in the number of transmitter-receiver pairs. The DoF achievability problem ...
详细信息
It is known that the problem of maximizing the sum degrees of freedom (DoF) for an arbitrary MIMO network without symbol extension is NP-hard in the number of transmitter-receiver pairs. The DoF achievability problem is also NP-hard if each transmitter/receiver has at least three antennas, and is polynomial-time solvable if each transmitter/receiver has no more than two antennas. It was conjectured that for the special case of the symmetric network (where all the transmitters have the same number of antennas and all the receivers have the same number of antennas), polynomial-time algorithms might exist for these two problems. In this paper, we show that the conjecture holds only in a very limited sense. We also show that for two important special cases of the symmetric network, both problems are polynomial-time solvable if the number of antennas at each transmitter/receiver is no more than two, and generally are NP-hard otherwise.
Given a set X and a collection D1, D2, ..., Dm of its nonempty subsets,consider the system of abstract inclusions x∈Dj, j∈Nm={1,2,...,m}, (1) System (1) is notnecessarily consistent; i.e., the case ∩Dj=φ is admiss...
详细信息
Given a set X and a collection D1, D2, ..., Dm of its nonempty subsets,consider the system of abstract inclusions x∈Dj, j∈Nm={1,2,...,m}, (1) System (1) is notnecessarily consistent; i.e., the case ∩Dj=φ is admissible. A finite sequence Q = (x1,x2,..., xq)satisfying the condition |{i: xi∈Dj}|
In a wide sense, easy test generation (ETG) circuits can be considered as design for testability (DFT) circuits. However most of the DFT techniques presented so far in the literature are attempts to ease test applicat...
详细信息
In a wide sense, easy test generation (ETG) circuits can be considered as design for testability (DFT) circuits. However most of the DFT techniques presented so far in the literature are attempts to ease test application. Major disadvantages with these DFT techniques are degradation of circuit performance, and often the requirement of a long and continuous test mode. However, an ETG circuit attempts to make test generation easier without any significant degradation of circuit performance, and the test mode can be divided into pieces to fit the requirement of real-time systems. The paper presents two important types of PLA design techniques which reduce the computational complexity for test generation. An O(n) ETG PLA is defined, and a sufficient condition for O(n2) ETG PLAs is also obtained. It is shown that the easily testable PLAs introduced by Bozorgui-Nesbat and McCluskey are O(n2) ETG PLAs.
Golf is a solitaire game, where the object is to move all cards from a 5 x 8 rectangular layout of cards to the foundation. A top card in each column may be moved to the foundation if it is either one rank higher or l...
详细信息
Golf is a solitaire game, where the object is to move all cards from a 5 x 8 rectangular layout of cards to the foundation. A top card in each column may be moved to the foundation if it is either one rank higher or lower than the top card of the foundation. If no cards may be moved, then the top card of the stock may be moved to the foundation. We prove that the generalized version of Golf Solitaire is NP-complete.
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intrac...
详细信息
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that despite the limitations our problems are also intractable, namely, we show that checking whether the maximal consistent frequency of a query is larger than a given threshold is NP-complete and that evaluating the Maximum Entropy estimate of a query is PP-hard. We also prove that checking consistency is NP-complete. (c) 2006 Elsevier B.V. All rights reserved.
This paper analyzes the computational complexity of set membership identification of Hammerstein and Wiener systems. Its main results show that, even in cases where a portion of the plant is known, the problems are ge...
详细信息
This paper analyzes the computational complexity of set membership identification of Hammerstein and Wiener systems. Its main results show that, even in cases where a portion of the plant is known, the problems are generically NP-hard both in the number of experimental data points and in the number of inputs (Wiener) or outputs (Hammerstein) of the nonlinearity. These results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point Out the need for developing computationally tractable relaxations. (C) 2008 Elsevier Ltd. All rights reserved.
A determinant decision diagram (DDD) uses a binary decision diagram (BDD) to calculate a determinant symbolically, which is then applied for symbolic circuit analysis. The efficiency of such a technique is determined ...
详细信息
A determinant decision diagram (DDD) uses a binary decision diagram (BDD) to calculate a determinant symbolically, which is then applied for symbolic circuit analysis. The efficiency of such a technique is determined mainly by a symbol ordering scheme. Finding an optimal symbol order is an non-deterministic polynomial-time hard problem in the practice of BDD. So far, it is unknown what an optimal order is for a general sparse matrix. This brief shows that a row-wise (or column-wise) order is an optimal BDD order for full matrices in the sense that the DDD graph constructed has the minimum number of vertices (i.e., the DDD size). The optimal DDD size is proven to be (n . 2(n-1)) for an n x n full matrix. This size provides a DDD complexity measure that has rarely been investigated in the literature.
暂无评论