scholarly journals Computational complexity of the quantum separability problem

2007 ◽  
Vol 7 (4) ◽  
pp. 336-370
Author(s):  
L.M. Ioannou
Keyword(s):  
Computational Complexity ◽  
Semidefinite Programming ◽  
Comprehensive Treatment ◽  
Optimal Point ◽  
Deterministic Algorithms ◽  
Separability Problem ◽  
Np Complete ◽  
Quantum De Finetti Theorem ◽  
The One ◽  
Np Hardness

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or \emph{separable}, state. This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic (as opposed to randomized) computational complexity. First, I review the one-sided tests for separability, paying particular attention to the semidefinite programming methods. Then, I discuss various ways of formulating the quantum separability problem, from exact to approximate formulations, the latter of which are the paper's main focus. I then give a thorough treatment of the problem's relationship with NP, NP-completeness, and co-NP. I also discuss extensions of Gurvits' NP-hardness result to strong NP-hardness of certain related problems. A major open question is whether the NP-contained formulation (QSEP) of the quantum separability problem is Karp-NP-complete; QSEP may be the first natural example of a problem that is Turing-NP-complete but not Karp-NP-complete. Finally, I survey all the proposed (deterministic) algorithms for the quantum separability problem, including the bounded search for symmetric extensions (via semidefinite programming), based on the recent quantum de Finetti theorem \cite{DPS02,DPS04,qphCKMR06}; and the entanglement-witness search (via interior-point algorithms and global optimization) \cite{ITCE04,IT06}. These two algorithms have the lowest complexity, with the latter being the best under advice of asymptotically optimal point-coverings of the sphere.

scholarly journals P Systems with Evolutional Communication and Division Rules

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 327
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Membrane Computing ◽  
P Systems ◽  
Membrane Systems ◽  
Sat Problem ◽  
Complete Problem ◽  
Intractable Problems ◽  
Np Complete ◽  
The One

A widely studied field in the framework of membrane computing is computational complexity theory. While some types of P systems are only capable of efficiently solving problems from the class P, adding one or more syntactic or semantic ingredients to these membrane systems can give them the ability to efficiently solve presumably intractable problems. These ingredients are called to form a frontier of efficiency, in the sense that passing from the first type of P systems to the second type leads to passing from non-efficiency to the presumed efficiency. In this work, a solution to the SAT problem, a well-known NP-complete problem, is obtained by means of a family of recognizer P systems with evolutional symport/antiport rules of length at most (2,1) and division rules where the environment plays a passive role; that is, P systems from CDEC^(2,1). This result is comparable to the one obtained in the tissue-like counterpart, and gives a glance of a parallelism and the non-evolutionary membrane systems with symport/antiport rules.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

THE HOSOYA INDEX OF GRAPHS FORMED BY A FRACTAL GRAPH

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950135 ◽  
Author(s):  
JIA-BAO LIU ◽  
JING ZHAO ◽  
JIE MIN ◽  
JINDE CAO
Keyword(s):  
Computational Complexity ◽  
Hosoya Index ◽  
Initial Graph ◽  
Np Complete

The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].

scholarly journals Stable roommates with narcissistic, single-peaked, and single-crossing preferences

2020 ◽  
Vol 34 (2) ◽  
Author(s):  
Robert Bredereck ◽  
Jiehua Chen ◽  
Ugo Paavo Finnendahl ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Structural Property ◽  
Incomplete Preferences ◽  
Two Agents ◽  
Single Crossing ◽  
Np Complete

Abstract The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e., every agent can be matched with any other agent) or incomplete preferences, with ties (i.e., two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommates that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity—Stable Roommates remains NP-complete.

scholarly journals Neural Network Approach to MPPT Control and Irradiance Estimation

2020 ◽  
Vol 10 (15) ◽  
pp. 5051
Author(s):  
Žarko Zečević ◽  
Maja Rolevski
Keyword(s):  
Neural Network ◽  
Computational Complexity ◽  
Low Complexity ◽  
Maximum Power ◽  
Photovoltaic Module ◽  
Neural Network Approach ◽  
Point Tracking ◽  
The Neural Network ◽  
Power Point ◽  
The One

Photovoltaic (PV) modules require maximum power point tracking (MPPT) algorithms to ensure that the amount of power extracted is maximized. In this paper, we propose a low-complexity MPPT algorithm that is based on the neural network (NN) model of the photovoltaic module. Namely, the expression for the output current of the NN model is used to derive the analytical, iterative rules for determining the maximal power point (MPP) voltage and irradiance estimation. In this way, the computational complexity is reduced compared to the other NN-based MPPT methods, in which the optimal voltage is predicted directly from the measurements. The proposed algorithm cannot instantaneously determine the optimal voltage, but it contains a tunable parameter for controlling the trade-off between the tracking speed and computational complexity. Numerical results indicate that the relative error between the actual maximum power and the one obtained by the proposed algorithm is less than 0.1%, which is up to ten times smaller than in the available algorithms.

scholarly journals Computing the Interleaving Distance is NP-Hard

2019 ◽  
Vol 20 (5) ◽  
pp. 1237-1271 ◽  
Author(s):  
Håvard Bakke Bjerkevik ◽  
Magnus Bakke Botnan ◽  
Michael Kerber
Keyword(s):  
Computational Complexity ◽  
Complete Characterization ◽  
Np Hard ◽  
Slight Improvement ◽  
Approximation Factor ◽  
Distance Computation ◽  
Persistence Modules ◽  
Np Complete ◽  
Interleaving Distance

Abstract We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are 1-interleaved is NP-complete, already for bigraded, interval decomposable modules. Our proof is based on previous work showing that a constrained matrix invertibility problem can be reduced to the interleaving distance computation of a special type of persistence modules. We show that this matrix invertibility problem is NP-complete. We also give a slight improvement in the above reduction, showing that also the approximation of the interleaving distance is NP-hard for any approximation factor smaller than 3. Additionally, we obtain corresponding hardness results for the case that the modules are indecomposable, and in the setting of one-sided stability. Furthermore, we show that checking for injections (resp. surjections) between persistence modules is NP-hard. In conjunction with earlier results from computational algebra this gives a complete characterization of the computational complexity of one-sided stability. Lastly, we show that it is in general NP-hard to approximate distances induced by noise systems within a factor of 2.

A fast algorithm for sparse multichannel blind deconvolution

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. V7-V16 ◽  
Author(s):  
Kenji Nose-Filho ◽  
André K. Takahata ◽  
Renato Lopes ◽  
João M. T. Romano
Keyword(s):  
Computational Complexity ◽  
Loss Function ◽  
Fast Algorithm ◽  
Blind Deconvolution ◽  
Synthetic Data ◽  
Minimum Entropy ◽  
Data Set ◽  
Robust Solution ◽  
Marine Data ◽  
The One

We have addressed blind deconvolution in a multichannel framework. Recently, a robust solution to this problem based on a Bayesian approach called sparse multichannel blind deconvolution (SMBD) was proposed in the literature with interesting results. However, its computational complexity can be high. We have proposed a fast algorithm based on the minimum entropy deconvolution, which is considerably less expensive. We designed the deconvolution filter to minimize a normalized version of the hybrid [Formula: see text]-norm loss function. This is in contrast to the SMBD, in which the hybrid [Formula: see text]-norm function is used as a regularization term to directly determine the deconvolved signal. Results with synthetic data determined that the performance of the obtained deconvolution filter was similar to the one obtained in a supervised framework. Similar results were also obtained in a real marine data set for both techniques.

scholarly journals LOGICS AND ALGEBRAS FOR MULTIPLE PLAYERS

2010 ◽  
Vol 3 (3) ◽  
pp. 485-519 ◽  
Author(s):  
LOES OLDE LOOHUIS ◽  
YDE VENEMA
Keyword(s):  
Computational Complexity ◽  
Winning Strategy ◽  
Boolean Algebras ◽  
Game Theoretic ◽  
Np Complete ◽  
Game Theoretic Semantics ◽  
Stone’S Theorem

We study a generalization of the standard syntax and game-theoretic semantics of logic, which is based on a duality between two players, to a multiplayer setting. We define propositional and modal languages of multiplayer formulas, and provide them with a semantics involving a multiplayer game. Our focus is on the notion of equivalence between two formulas, which is defined by saying that two formulas are equivalent if under each valuation, the set of players with a winning strategy is the same in the two respective associated games. We provide a derivation system which enumerates the pairs of equivalent formulas, both in the propositional case and in the modal case. Our approach is algebraic: We introduce multiplayer algebras as the analogue of Boolean algebras, and show, as the corresponding analog to Stone’s theorem, that these abstract multiplayer algebras can be represented as concrete ones which capture the game-theoretic semantics. For the modal case we prove a similar result. We also address the computational complexity of the problem whether two given multiplayer formulas are equivalent. In the propositional case, we show that this problem is co-NP-complete, whereas in the modal case, it is PSPACE-hard.

DISCRETE KINETIC CELLULAR MODELS OF TUMORS IMMUNE SYSTEM INTERACTIONS

1996 ◽  
Vol 06 (08) ◽  
pp. 1187-1209 ◽  
Author(s):  
M. LO SCHIAVO
Keyword(s):  
Immune System ◽  
Computational Complexity ◽  
Differential Equations ◽  
Statistical Mechanics ◽  
Tumor Cells ◽  
Kinetic Modelling ◽  
Immune Defence ◽  
Control Parameters ◽  
Cellular Models ◽  
The One

This paper deals with a kinetic modelling of the cellular dynamics of tumors interacting with an active immune defence system. The analysis starts from the model proposed in Refs. 4 and 5 where a kinetic (cellular) theory of the interactions and competition between tumor cells and immune system is developed in a framework similar to the one of nonlinear statistical mechanics. The class of models proposed in this paper replaces the system of integro-differential equations by a system of ordinary differential equations. This has several advantages. Firstly, it allows immediate interpretations of the control parameters and is characterized by a relatively lower computational complexity. Further, some interesting periodicity properties of the solutions are characterized.

An Efficient Technique to Ensure the Logical Consistency of Interacting Knowledge Bases

1997 ◽  
Vol 06 (01) ◽  
pp. 27-36 ◽  
Author(s):  
Bertrand Mazure ◽  
Lakhdar Saïs ◽  
Éric Grégoire
Keyword(s):  
Local Search ◽  
Fundamental Problem ◽  
Real Life ◽  
Knowledge Bases ◽  
The Other ◽  
Logical Consistency ◽  
Complete Problem ◽  
Np Complete ◽  
The One ◽  
Cooperative Knowledge

In this paper, we address a fundamental problem in the formalization and implementation of cooperative knowledge bases: the difficulty of preserving consistency while interacting or combining them. Indeed, knowledge bases that are individually consistent can exhibit global inconsistency. This stumbling-block problem is an even more serious drawback when knowledge and reasoning are expressed using logical terms. Indeed, on the one hand, two contradictory pieces of information lead to global inconsistency under complete standard rules of deduction: every assertion and its contrary can be deduced. On the other hand, checking the logical consistency of a propositional knowledge base is an NP-complete problem and is often out of reach for large real-life applications. In this paper, a new practical technique to locate inconsistent interacting pieces of information is presented in the context of cooperative logical knowledge bases. Based on a recently discovered heuristic about the work performed by local search techniques, it can be applied in the context of large interacting knowledge bases.

Sign in / Sign up

Export Citation Format

Share Document