22,776 research outputs found
A Composition Theorem for Randomized Query Complexity via Max-Conflict Complexity
For any relation f subseteq {0,1}^n x S and any partial Boolean function g:{0,1}^m -> {0,1,*}, we show that R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * sqrt{R_{1/3}(g)})where R_epsilon(*) stands for the bounded-error randomized query complexity with error at most epsilon, and f o g^n subseteq ({0,1}^m)^n x S denotes the composition of f with n instances of g.
The new composition theorem is optimal, at least, for the general case of relational problems: A relation f_0 and a partial Boolean function g_0 are constructed, such that R_{4/9}(f_0) in Theta(sqrt n), R_{1/3}(g_0)in Theta(n) and R_{1/3}(f_0 o g_0^n) in Theta(n).
The theorem is proved via introducing a new complexity measure, max-conflict complexity, denoted by bar{chi}(*). Its investigation shows that bar{chi}(g) in Omega(sqrt{R_{1/3}(g)}) for any partial Boolean function g and R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * bar{chi}(g)) for any relation f, which readily implies the composition statement. It is further shown that bar{chi}(g) is always at least as large as the sabotage complexity of g
A composition theorem for randomized query complexity via max conflict complexity
Let stand for the bounded-error randomized query
complexity with error . For any relation and partial Boolean function ,
we show that , where is
the composition of and . We give an example of a relation and
partial Boolean function for which this lower bound is tight.
We prove our composition theorem by introducing a new complexity measure, the
max conflict complexity of a partial Boolean function . We
show for any (partial) function
and ; these
two bounds imply our composition result. We further show that is
always at least as large as the sabotage complexity of , introduced by
Ben-David and Kothari
Reconfigurable Lattice Agreement and Applications
Reconfiguration is one of the central mechanisms in distributed systems. Due to failures and connectivity disruptions, the very set of service replicas (or servers) and their roles in the computation may have to be reconfigured over time. To provide the desired level of consistency and availability to applications running on top of these servers, the clients of the service should be able to reach some form of agreement on the system configuration. We observe that this agreement is naturally captured via a lattice partial order on the system states. We propose an asynchronous implementation of reconfigurable lattice agreement that implies elegant reconfigurable versions of a large class of lattice abstract data types, such as max-registers and conflict detectors, as well as popular distributed programming abstractions, such as atomic snapshot and commit-adopt
PS-TRUST: Provably Secure Solution for Truthful Double Spectrum Auctions
Truthful spectrum auctions have been extensively studied in recent years.
Truthfulness makes bidders bid their true valuations, simplifying greatly the
analysis of auctions. However, revealing one's true valuation causes severe
privacy disclosure to the auctioneer and other bidders. To make things worse,
previous work on secure spectrum auctions does not provide adequate security.
In this paper, based on TRUST, we propose PS-TRUST, a provably secure solution
for truthful double spectrum auctions. Besides maintaining the properties of
truthfulness and special spectrum reuse of TRUST, PS-TRUST achieves provable
security against semi-honest adversaries in the sense of cryptography.
Specifically, PS-TRUST reveals nothing about the bids to anyone in the auction,
except the auction result. To the best of our knowledge, PS-TRUST is the first
provably secure solution for spectrum auctions. Furthermore, experimental
results show that the computation and communication overhead of PS-TRUST is
modest, and its practical applications are feasible.Comment: 9 pages, 4 figures, submitted to Infocom 201
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