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About 8,960 papers for “query complexity”

Query complexity and symetries

NESME, Vincent, KOIRAN, Pascal, PORTIER, Natacha · OpenGrey (Institut de l'Information Scientifique et Technique) · 2007

Ces travaux portent sur l'étude de la complexité en requêtes de problèmes symétriques, dans les cadres du calcul probabiliste classique et du calcul quantique. Il est montré, dans le cas quantique, une application de la méthode de bornes inférieures dite "polynomiale" au calcul de la complexité en requête des problèmes de sous-groupes cachés abéliens, via la technique de "symétrisation". Dans le cas du calcul probabiliste, sous une hypothèse de "symétrie transitive" des problèmes, il est donné une formule combinatoire permettant de calculer la complexité en requêtes exacte du meilleur algorithme non-adaptatif. De plus, il est mis en évidence que sous certaines hypothèses de symétries, ce meilleur algorithme non-adaptatif est optimal même parmi les algorithmes probabilistes plus généraux, ce qui donne pour la classe de problèmes correspondante une expression exacte de la complexité en requêtes.

Cited by 0

Unambiguous parity-query complexity

Dmytro Gavinsky · arXiv (Cornell University) · 2024

We give a lower bound of $Ω(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value is "0" if the Hamming weight of the input is at most n/3, is "1" if the weight is at least 2n/3, and may be arbitrary otherwise.

Cited by 0Open access

Quantum Bounded Query Complexity

Buhrman, Harry, van Dam, Wim · arXiv (Cornell University) · 1999

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function classes. For decision problems and function classes we obtain the following results: o P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one complete for PP have the property that FP_||^A is included in FEQP^A[1]. In general we prove that for any set A there is a set X such that FP^A is included in FEQP^X[1], establishing that no set is superterse in the quantum setting.

Cited by 0Open access

Query Complexity with Unknowns

Nikhil S. Mande, Karteek Sreenivasaiah · arXiv (Cornell University) · 2024

We initiate the study of a new model of query complexity of Boolean functions where, in addition to 0 and 1, the oracle can answer queries with ``unknown''. The query algorithm is expected to output the function value if it can be conclusively determined by the partial information gathered, and it must output ``unknown'' if not. We formalize this model by using Kleene's strong logic of indeterminacy on three variables to capture unknowns. We call this model the `u-query model'. We relate the query complexity of functions in the new u-query model with their analogs in the standard query model. We show an explicit function that is exponentially harder in the u-query model than in the usual query model. We give sufficient conditions for a function to have u-query complexity asymptotically the same as its query complexity. Using u-query analogs of the combinatorial measures of sensitivity, block sensitivity, and certificate complexity, we show that deterministic, randomized, and quantum u-query complexities of all total Boolean functions are polynomially related to each other, just as in the usual query models.

Cited by 0Open access

Quantum bounded query complexity

Harry Buhrman, Wim van Dam · ArXiv.org · 2003

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query, complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function classes. For decision problems and function classes we obtain the following results: P/sub /spl par///sup NP[2k]//spl sube/EQP/sub /spl par///sup NP[k]/; P/sub /spl par///sup NP[2k+1-2]//spl sube/EQP/sup NP[k]/; FP/sub /spl par///sup NP[2k=1-2]//spl sube/FEQP/sup NP[2k]/; FP/sub /spl par///sup NP/spl sube/FEQP(NP[Olog n)]/. For sets A that are many-one complete for PSPACE or EXP we show that Fp/sup A//spl sube/FEQP/sup A[1]/. Sets A that are many-one complete for PP have the property that FP/sub /spl par///sup A//spl sube/FEQP/sup A[1]/. In general we prove that for any set A there is a set X such that FP/sup A//spl sube/FEQP/sup X[1]/, establishing that no set is superterse in the quantum setting.

Cited by 10Open access

Nonadaptive quantum query complexity

Ashley Montanaro · arXiv (Cornell University) · 2009

We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that computes some total boolean function depending on n variables must make Omega(n) queries to the input in total. Second, we show that, if there exists a quantum algorithm that uses k nonadaptive oracle queries to learn which one of a set of m boolean functions it has been given, there exists a nonadaptive classical algorithm using O(k log m) queries to solve the same problem. Thus, in the nonadaptive setting, quantum algorithms can achieve at most a very limited speed-up over classical query algorithms.

Cited by 0Open access

Quantum query complexity revisited

Daniel Preda · DSpace@MIT (Massachusetts Institute of Technology) · 2003

Thesis (M.Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.

Cited by 0Open access

Average-Case Quantum Query Complexity

Ronald De Wolf · 1999

We compare classical and quantum query complexities of total Boolean functions. It has been shown that for worst-case complexity, the gap between quantum and classical can be at most polynomial (BBCMW98). We give (non-uniform) distributions where the gap for average-case complexity of the OR-function can be exponential or even larger. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.

Cited by 0

Quantum speedups in query complexity

Ben David, Shalev · DSpace@MIT (Massachusetts Institute of Technology) · 2017

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.

Cited by 0Open access

Average-Case Quantum Query Complexity

Andris Ambainis, R.M. de Wolf · UvA-DARE (University of Amsterdam) · 1999

We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.

Cited by 9Open access

On exact quantum query complexity

Montanaro, Ashley, Jozsa, Richard, Mitchison, Graeme · arXiv (Cornell University) · 2011

We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities of pairs of bits. We also characterise the model of nonadaptive exact quantum query complexity in terms of coding theory and completely characterise the query complexity of symmetric boolean functions in this context. These results were originally inspired by numerically solving the semidefinite programs characterising quantum query complexity for small problem sizes. We include numerical results giving the optimal success probabilities achievable by quantum algorithms computing all boolean functions on up to 4 bits, and all symmetric boolean functions on up to 6 bits.

Cited by 0Open access

Structural complexity and query complexity for total problems

VERHOEVEN, Yves, SANTHA, Miklos · OpenGrey (Institut de l'Information Scientifique et Technique) · 2005

Dans cette thèse, nous abordons des problèmes de complexité structurelle, traitant de la classification des problèmes en fonction de leurs difficultés relatives, et nous nous intéressons aussi à l'existence d'une solution à un problème plus concret d'algorithmique en-ligne. Suivant cette dichotomie, dans la première partie de cette thèse nous étudions des problèmes de la classe des problèmes totaux TFNP, à savoir les problèmes de Sperner et la recherche de minimum local. Nous montrons les complétudes de problèmes de Sperner localement 2-dimensionnels dans les classes d'arguments de parité PPA, PPAD et PPADS. Nous améliorons ainsi des résultats de Papadimitriou et Grigni. Nous étudions ensuite le nombre de requêtes, au sens classique et au sens quantique, nécessaires pour résoudre un problème de Sperner en dimension arbitraire sur une pseudo-variété ; nous prouvons une borne inférieure ainsi qu'une borne supérieure correspondant à la complexité d'un algorithme, cette dernière étant optimale pour un cas précédemment étudié par Crescenzi et Silvestri. Enfin, nous donnons deux algorithmes, un classique et un quantique, pour déterminer la position d'un minimum local d'une fonction définie sur les sommets d'un graphe. Les analyses de nos deux algorithmes sont fondées sur l'existence de séparateurs de petite taille dans les graphes, et nous montrons un tel résultat qui améliore un résultat antérieur de Gilbert, Hutchinson et Tarjan. Dans la seconde partie de la thèse, nous nous intéressons à l'existence d'un algorithme en-ligne sans mémoire pour le problème CNN. Notre résultat généralise et améliore un résultat antérieur de Koutsoupias et Taylor.

Cited by 0Open access

Unbounded Error Quantum Query Complexity

Ashley Montanaro, Harumichi Nishimura, Rudy Raymond · arXiv (Cornell University) · 2007

This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication complexity model, the unbounded error quantum query complexity is exactly half of its classical counterpart for any (partial or total) Boolean function. Moreover, we show that the "black-box" approach to convert quantum query algorithms into communication protocols by Buhrman-Cleve-Wigderson [STOC'98] is optimal even in the unbounded error setting. We also study a setting related to the unbounded error model, called the weakly unbounded error setting, where the cost of a query algorithm is given by q+log(1/2(p-1/2)), where q is the number of queries made and p>1/2 is the success probability of the algorithm. In contrast to the case of communication complexity, we show a tight Theta(log n) separation between quantum and classical query complexity in the weakly unbounded error setting for a partial Boolean function. We also show the asymptotic equivalence between them for some well-studied total Boolean functions.

Cited by 0Open access

The complexity of query reliability

Erich Grädel, Yuri Gurevich, Colin Hirsch · 1998

Article The complexity of query reliability Share on Authors: Erich Grädel University of Technology Aachen University of Technology AachenView Profile , Yuri Gurevich Universtity of Michigan Universtity of MichiganView Profile , Colin Hirsch University of Technology Aachen University of Technology AachenView Profile Authors Info & Claims PODS '98: Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systemsMay 1998 Pages 227–234https://doi.org/10.1145/275487.295124Online:01 May 1998Publication History 52citation335DownloadsMetricsTotal Citations52Total Downloads335Last 12 Months5Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Cited by 80