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Entanglement monotone derived from Grover's algorithm

Ofer Biham, Michael A. Nielsen, Tobias J. Osborne
2002 Physical Review A. Atomic, Molecular, and Optical Physics  
This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglement, the less well the  ...  More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability P_max that the search algorithm  ...  Special thanks are also due to Jennifer Dodd for an exceptionally thorough reading of the manuscript, and many helpful suggestions on how to improve it.  ... 
doi:10.1103/physreva.65.062312 fatcat:bejkdouoo5c3vmphfrjdsdg27m

Logic-based interpretation of geometrically observable changes occurring in dynamic scenes

M. V. dos Santos, R. C. de Brito, H.-H. Park, P. Santos
2008 Applied intelligence (Boston)  
In this approach, a database state represents the available sensor data at a particular time instant.  ...  The work presented here is about employing a theory of updates to study geometrically observable changes that occur in spatial information about image sequences of a dynamic scene.  ...  An intuitive approach to obtain the transition predicates φ i , 1 ≤ i < k, is to input the first and second states to the transition oracle and obtain the set of predicates, say {a 1 , a 2 , · · · , a  ... 
doi:10.1007/s10489-008-0120-4 fatcat:elq2arjdi5hefjjyqbxpk5tulm

Approximation to measurable functions and its relation to probabilistic computation

Ker-I Ko
1986 Annals of Pure and Applied Logic  
The computational complexity of the Lebesgue integral of polynomial-time approximable functions is studied and related to the question "FP = #P?".  ...  The approximation method uses a model of oracle Turing machines, and so the computational complexity may be defined in a natural way.  ...  Another possible extension of our theory is to follow Pour-El and Richards's approach [23] to give an axiomatic treatment of the computational complexity on Banach spaces and L*-spaces.  ... 
doi:10.1016/0168-0072(86)90005-9 fatcat:fwmlrnsx4jcopmh7uyc2otyxti

Favor Short Dependencies: Parsing with Soft and Hard Constraints on Dependency Length [chapter]

Jason Eisner, Noah A. Smith
2010 Text, Speech and Language Technology  
We show how to parse this language in O(n) time, using a novel chart parsing algorithm with a low grammar constant (rather than an impractically large finite-state recognizer with an exponential grammar  ...  In lexicalized phrase-structure or dependency parses, a word's modifiers tend to fall near it in the string. This fact can be exploited by parsers.  ...  They also thank an anonymous reviewer for suggesting the German experiments.  ... 
doi:10.1007/978-90-481-9352-3_8 fatcat:n3otracsgzgozi6dwe7bemzdja

Best of Two Local Models: Local Centralized and Local Distributed Algorithms [article]

Guy Even, Moti Medina, Dana Ron
2014 arXiv   pre-print
The recursive centralized local improvement technique by Nguyen and Onak onak2008 is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching.  ...  Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over  ...  It is based on a recursive oracle O i . The input to oracle O i is an edge e ∈ E, and the output is a bit that indicates whether e ∈ M i .  ... 
arXiv:1402.3796v3 fatcat:ub2t6c3gkrfenmt4wkknbuekzm

Rare Speed-up in Automatic Theorem Proving Reveals Tradeoff Between Computational Time and Information Value [article]

Santiago Hernández-Orozco, Francisco Hernández-Quiroz, Hector Zenil, Wilfried Sieg
2015 arXiv   pre-print
We advance formal definitions for these concepts by way of a notion of normality related to an expected (optimal) theoretical speedup when adding useful information (other theorems as axioms), as compared  ...  We show that strategies implemented in automatic theorem proving involve an interesting tradeoff between execution speed, proving speedup/computational time and usefulness of information.  ...  sequence on the path from t to β as proof.  ... 
arXiv:1506.04349v1 fatcat:w6hgogpkzna75oogn2xfvsecky

A Combinatorial Problem Arising From Ecology: the Maximum Empower Problem [article]

Chams Lahlou, Laurent Truffet
2018 arXiv   pre-print
In this paper we show that the Maximum Empower Problem can be solved by finding a maximum weighted clique in a cograph, which leads to an exponential-time algorithm in the worst-case.  ...  The roots of these notions trace back to the 50's (with the work of H. T. Odum and R. C. Pinkerton) and is becoming now an important sustainability indicator in the ecologist community.  ...  To do so, it suffices to compute the shortest paths from l to every node i in the graph G where each arc is reversed.  ... 
arXiv:1802.05974v1 fatcat:znnpmsjlc5bnvfnm6nwtzhxleu

Quantum computing and hidden variables

Scott Aaronson
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
Toward this end, we construct a new hidden-variable theory that is both robust to small perturbations and indifferent to the identity operation, by exploiting an unexpected connection between unitary matrices  ...  For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final  ...  This work was done while the author was a PhD student at UC Berkeley, supported by an NSF Graduate Fellowship.  ... 
doi:10.1103/physreva.71.032325 fatcat:u42zfmxzzzcapagmdjvqmpouaq

Interpretations of the Web of Data [article]

Marko A. Rodriguez
2009 arXiv   pre-print
URIs are used to identify resources and RDF is used to relate resources.  ...  The emerging Web of Data utilizes the web infrastructure to represent and interrelate data.  ...  Starting from i a "fan-out" search for j is executed where at each time step, adjacent vertices are traversed to. The first path that reaches j is the shortest path from i to j.  ... 
arXiv:0905.3378v2 fatcat:iz47mtqrpncuff6hqvd3m6oqai

In Praise of Numerical Computation [chapter]

Chee K. Yap
2009 Lecture Notes in Computer Science  
I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms' design.  ...  Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona.  ...  This is illustrated by Figure 1 which shows two disc obstacles A, B, and two possible shortest paths from p −p q A B Two Discs Figure 1 : Shortest path from p to q p to q.  ... 
doi:10.1007/978-3-642-03456-5_26 fatcat:fvfcb4q6inelfcvsd44nbfpdza

The axiomatic power of Kolmogorov complexity

Laurent Bienvenu, Andrei Romashchenko, Alexander Shen, Antoine Taveneaux, Stijn Vermeeren
2014 Annals of Pure and Applied Logic  
One classical (and well studied) approach is to add to some theory T an axiom that claims the consistency of T .  ...  We then study the axiomatic power of the statements of type "the Kolmogorov complexity of x exceeds n" (where x is some string, and n is some integer) in general.  ...  Special thanks go to Ilya Razenshteyn for bringing Richard Lipton's post [LR11] to our attention and to Chris Porter for many helpful comments on preliminary versions of this paper.  ... 
doi:10.1016/j.apal.2014.04.009 fatcat:yobwzltofvgshdvjmojm5sfzs4

Provably Safe Artificial General Intelligence via Interactive Proofs

Kristen Carlson
2021 Philosophies  
In toto, IPS provides a way to reduce AGIn ↔ AGIn+1 interaction hazards to an acceptably low level.  ...  Numerous paths toward human extinction or subjugation have been identified.  ...  approach [14] .  ... 
doi:10.3390/philosophies6040083 fatcat:beibzummbngrhacbxv3yeuit6m

Introduction to the Theory of Complexity

V. J. Rayward-Smith
1995 Journal of the Operational Research Society  
The information in this book is distributed on an "As is" basis, without warranty.  ...  Although every precaution has been taken in the preparation of this work, the authors shall not have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused  ...  We would like to thank the students who were exposed to the preliminary versions of the chapters and who contributed their observations to improve the quality of the presentation.  ... 
doi:10.1057/jors.1995.211 fatcat:rx2m7i3vyreaflkxrbmuh5kbhu

Subject index volumes 1–200

1999 Theoretical Computer Science  
an isomorphism type, 3630 distance queries, 2657 distances, 2234, 2657 distinguishing subsequence, 1530 shortest maximal common non-supersequence, 2734 subsequence, 2734 shortest paths, 1577.2006  ...  , 2564 problem, 305 1 shortest tours, 1250 shortest vector, 2392 in a two-dimensional lattice, 3397 shortest word, 932 of minimal rank, 1141 shortest words, 2114 shortest-path planning, 2655  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Diverse Consequences of Algorithmic Probability [article]

Eray Özkural
2011 arXiv   pre-print
We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline.  ...  We also relate to our own work in incremental machine learning and philosophy of complexity.  ...  The axiomatic approach was seen counter-productive by some leading researchers in the past.  ... 
arXiv:1107.2788v2 fatcat:f2zj6n7txra53jsgk7iumqq3ja
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