We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than O(max(N, N3q-1/q)), where N is t...
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ISBN:
(纸本)9783030504205;9783030504199
We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than O(max(N, N3q-1/q)), where N is the number of nodes and q is the dimensionality of the singularity. In particular, we show that this formula does not change depending on the spatial dimensionality of the mesh. We also show the relationship between the time complexity and the Kolmogorov dimension of the singularity.
We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that...
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We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility of revising the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of formal semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science.
We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machi...
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We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measurement and dissipative process. Moreover, we discovered that a chaos dynamics has very important role in quantum algorithm, that is useful to solve NP complete problem in polynomial time. In this paper, we introduce the GQTM and some applications. (C) 2011 Elsevier Inc. All rights reserved.
We revisit the computational complexity of decision problems about existence of Nash equilibria in multi-player games satisfying certain natural properties. Such problems have generally been shown to be complete for t...
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ISBN:
(纸本)9783031432538;9783031432545
We revisit the computational complexity of decision problems about existence of Nash equilibria in multi-player games satisfying certain natural properties. Such problems have generally been shown to be complete for the complexity class.R, that captures the complexity of the decision problem for the Existential Theory of the Reals. For most of these problems, we show that their complexity remains unchanged even when restricted to win-lose games, where all utilities are either 0 or 1.
Recent development of portable devices and prevalence of high-throughput communication infrastructures make the video encoding in portable devices on high demand. However, its computational complexity makes the implem...
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ISBN:
(纸本)9781424444632
Recent development of portable devices and prevalence of high-throughput communication infrastructures make the video encoding in portable devices on high demand. However, its computational complexity makes the implementation of real-time video encoder on portable devices extremely difficult. Many fast algorithms to solve the problems are not efficient from the view point of worst workload since they consider only reduction of average computational complexity. Moreover., since the amount of reduction of computational complexity highly depends on video sequence, fixed fast algorithms cannot always achieve their full potential for real-time encoding. In this paper, we analyze the complexity of H.264/AVC video coding tools, and develop two parameters for complexity control. Consequently, we design a power-aware complexity scalable encoding scheme implementable on embedded system. Using our target embedded system, the proposed method is verified to save power by about 50%.
This paper proposes a frequency averaging method to reduce computational complexity for the implementation of a two-channel parameterized multichannel Wiener filter (PMWF) algorithm. Experimental results show that the...
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ISBN:
(纸本)9781538630259
This paper proposes a frequency averaging method to reduce computational complexity for the implementation of a two-channel parameterized multichannel Wiener filter (PMWF) algorithm. Experimental results show that the proposed algorithm can reduce the amount of computation by 40.24 % compared to the conventional PMWF algorithm while preserving speech quality after the speech enhancement.
For a long time modeling approaches to stochastic programming were dominated by scenario generation methods. Consequently the main computational effort went into development of decomposition type algorithms for solvin...
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ISBN:
(纸本)9789814324342
For a long time modeling approaches to stochastic programming were dominated by scenario generation methods. Consequently the main computational effort went into development of decomposition type algorithms for solving constructed large scale (linear) optimization problems. A different point of view emerged recently where computational complexity of stochastic programming problems was investigated from the point of view of randomization methods based on Monte Carlo sampling techniques. In that approach the number of scenarios is irrelevant and can be infinite. On the other hand, from that point of view there is a principle difference between computational complexity of two and multistage stochastic programming problems - certain classes of two stage stochastic programming problems can be solved with a reasonable accuracy and reasonable computational effort, while (even linear) multistage stochastic programming problems seem to be computationally intractable in general.
We present in this paper how to assess the network routing logical security policy of an Internet Service Provider network, through a reverse-engineering process performed on the network routers configurations. This p...
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ISBN:
(纸本)0769518869
We present in this paper how to assess the network routing logical security policy of an Internet Service Provider network, through a reverse-engineering process performed on the network routers configurations. This paper covers the definition of a network routing logical security policy, how to implement it in the network routers configurations, in addition it details the algorithms and their asymptotic time complexity required to assess this security policy.
We show that the satisfiability problem in core fragments of modal logics T, K4, and S4 in whose languages diamond modal operators are disallowed is NL-complete. Moreover, we provide deterministic procedures for satis...
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ISBN:
(纸本)9783030195700;9783030195694
We show that the satisfiability problem in core fragments of modal logics T, K4, and S4 in whose languages diamond modal operators are disallowed is NL-complete. Moreover, we provide deterministic procedures for satisfiability checking. We show that the above fragments correspond to certain core fragments of linear temporal logic, hence our results imply NL-completeness of the latter.
In physics, systems having three parts are typically much more difficult to analyze than those having just two. Even in classical mechanics, predicting the motion of three interacting celestial bodies remains an insur...
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In physics, systems having three parts are typically much more difficult to analyze than those having just two. Even in classical mechanics, predicting the motion of three interacting celestial bodies remains an insurmountable challenge while the analogous two-body problem has an elementary solution. It is as if just by adding a third party, a fundamental change occurs in the structure of the problem that renders it unsolvable. In this thesis, we demonstrate how such an effect is likewise present in the theory of quantum entanglement. In fact, the complexity differences between two-party and three-party entanglement become quite conspicuous when comparing the difficulty in deciding what state changes are possible for these systems when no additional entanglement is consumed in the transformation process. We examine this entanglement transformation question and its variants in the language of computational complexity theory, a powerful subject that formalizes the concept of problem difficulty. Since deciding feasibility of a specified bipartite transformation is relatively easy, this task belongs to the complexity class P. On the other hand, for tripartite systems, we find the problem to be NP-Hard, meaning that its solution is at least as hard as the solution to some of the most difficult problems humans have encountered. One can then rigorously defend the assertion that a fundamental complexity difference exists between bipartite and tripartite entanglement since unlike the former, the full range of forms realizable by the latter is incalculable (assuming P≠NP). However, similar to the three-body celestial problem, when one examines a special subclass of the problem—invertible transformations on systems having at least one qubit subsystem—we prove that the problem can be solved efficiently. As a hybrid of the two questions, we find that the question of tripartite to bipartite transformations can be solved by an efficient randomized algorithm. Our results are obtain
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