Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments

We prove a very general lower bound technique for quantum and randomized query complexity that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique generalizes the weighted and unweighted methods of Ambainis and the s...

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Vydané v:SIAM journal on computing Ročník 38; číslo 1; s. 46 - 62
Hlavní autori: Laplante, Sophie, Magniez, Frédéric
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2008
Predmet:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Boolean
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Mathematics
Methods
Miscellaneous
Order, lattices, ordered algebraic structures
Quantum computing
Queries
Sciences and techniques of general use
Theoretical computing
Lower bound
Input
Spectral method
Query
Kolmogorov complexity; 81P68
quantum computing
Kolmogorov complexity
query complexity
Boolean function
adversary method
lower bounds
68Q30
ISSN:0097-5397, 1095-7111
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Shrnutí:We prove a very general lower bound technique for quantum and randomized query complexity that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique generalizes the weighted and unweighted methods of Ambainis and the spectral method of Barnum, Saks, and Szegedy. As an immediate consequence of our main theorem, it can be shown that adversary methods can only prove lower bounds for Boolean functions $f$ in $O(\min(\sqrt{n C_0(f)},\sqrt{n C_1(f)}))$, where $C_0, C_1$ is the certificate complexity and $n$ is the size of the input.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/050639090