1

September 2017
Journal of the ACM (JACM): Volume 64 Issue 5, October 2017

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 12, Downloads (12 Months): 102, Downloads (Overall): 102

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function f on n = 2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R ...

**Keywords**:
query complexity, Decision trees, quantum algorithms

2

July 2017
CCC '17: Proceedings of the 32nd Computational Complexity Conference

**Publisher:** Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but only a few of these are known to be complete in the class. Before this ...

**Keywords**:
chevalley-warning theorem, combinatorial nullstellensatz, PPA

3

June 2016
STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 3

Downloads (6 Weeks): 1, Downloads (12 Months): 33, Downloads (Overall): 108

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We show that every algorithm for testing n -variate Boolean functions for monotonicityhas query complexity Ω( n 1/4 ). All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a result, the best previous lower bound for general (possibly adaptive) monotonicity testers was only Ω(log n ...

**Keywords**:
Adaptivity of query algorithms, Property Testing, Talagrand's Random DNF

4

June 2016
STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 2

Downloads (6 Weeks): 3, Downloads (12 Months): 48, Downloads (Overall): 115

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function f on n =2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R 0 ...

**Keywords**:
Monte Carlo, Randomized algorithms, Deterministic algorithms, Las Vegas, Quantum algorithms

5

January 2016
SODA '16: Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms

**Publisher:** Society for Industrial and Applied Mathematics

**Bibliometrics**:

Citation Count: 1

Downloads (6 Weeks): 1, Downloads (12 Months): 21, Downloads (Overall): 43

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In the k -junta testing problem, a tester has to efficiently decide whether a given function f : {0, 1} n → {0, 1} is a k -junta (i.e., depends on at most fc of its input bits) or is ε -far from any k -junta. Our main result is ...

6

September 2015
Quantum Information & Computation: Volume 15 Issue 11-12, September 2015

**Publisher:** Rinton Press, Incorporated

Given a random permutation f : [ N ] → [ N ] as a black box and y ε [ N ], we want to output x = f -1 ( y ). Supplementary to our input, we are given classical advice in the form of a pre-computed data ...

**Keywords**:
one-way function, random permutation, time-space tradeoff, quantum lower bound

7

June 2015
Computational Complexity: Volume 24 Issue 2, June 2015

**Publisher:** Birkhauser Verlag

In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function f on n variables that only depends on k variables, and, when restricted to them, equals some predefined function h. The task is to identify the variables the ...

**Keywords**:
68Q12, 81P68, combinatorial group testing, representation theory of the symmetric group, Quantum query algorithms, computational learning theory, semi-definite optimization

8

June 2014
CCC '14: Proceedings of the 2014 IEEE 29th Conference on Computational Complexity

**Publisher:** IEEE Computer Society

In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function f on n variables that only depends on k variables, and, when restricted to them, equals some predefined function h. The task is to identify the variables the ...

**Keywords**:
quantum query complexity, computational learning theory, group testing

9

June 2014
Computational Complexity: Volume 23 Issue 2, June 2014

**Publisher:** Birkhauser Verlag

We introduce a notion of the quantum query complexity of a certificate structure. This is a formalization of a well-known observation that many quantum query algorithms only require the knowledge of the position of possible certificates in the input string, not the precise values therein. Next, we derive a dual ...

**Keywords**:
68Q12, 81P68, adversary method, k-sum problem, triangle problem, semidefinite optimization, Quantum computing, query algorithms

10

July 2013
ICALP'13: Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I

**Publisher:** Springer-Verlag

We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time complexity $\tilde{O}(n^{5/7})$, improving the previous $\tilde{O}(n^{3/4})$ and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors. The first algorithm is based on a connection between quantum walks and electric networks. ...

11

January 2013
ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 3

Downloads (6 Weeks): 1, Downloads (12 Months): 6, Downloads (Overall): 57

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We prove a tight quantum query lower bound Omega(n k/(k+1) ) for the problem of deciding whether there exist k numbers among n that sum up to a prescribed number, provided that the alphabet size is sufficiently large.

**Keywords**:
knapsack packing problem, quantum query complexity, orthogonal arrays

12

October 2012
FOCS '12: Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

**Publisher:** IEEE Computer Society

We present a quantum algorithm solving the k-distinctness problem in a less number of queries than the previous algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee, the algorithm doesn't require any prior information on the input, and the ...

**Keywords**:
quantum computing, query complexity

13

September 2012
ESA'12: Proceedings of the 20th Annual European conference on Algorithms

**Publisher:** Springer-Verlag

We use span programs to develop quantum algorithms for several graph problems. We give an algorithm that uses $O(n \sqrt d)$ queries to the adjacency matrix of an n -vertex graph to decide if vertices s and t are connected, under the promise that they either are connected by a ...

14

May 2012
STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 15

Downloads (6 Weeks): 2, Downloads (12 Months): 13, Downloads (Overall): 247

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Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the element distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph. ...

**Keywords**:
quantum algorithms

15

December 2008
Mathematical Methods in Computer Science: Essays in Memory of Thomas Beth

**Publisher:** Springer-Verlag

The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch bounds with equality is given and applied for the ...

16

July 2007
DLT'07: Proceedings of the 11th international conference on Developments in language theory

**Publisher:** Springer-Verlag

The regular language ( a + b )* a (the words in alphabet { a, b } having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automaton (QFA). Up to now, there have been introduced many ...

17

January 2006
SOFSEM'06: Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science

**Publisher:** Springer-Verlag

A new complexity measure for Boolean functions is introduced in this article. It has a link to the query algorithms: it stands between both polynomial degree and non-deterministic complexity on one hand and still is a lower bound for deterministic complexity. Some inequalities and counterexamples are presented and usage in ...