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Motivated by questions in lossy data compression and by theoretical considerations, the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data is examined. The focus is the behavior of the so-called ldquoplug-inrdquo estimator, which is simply the rate-distortion function of the empirical distribution of the observed data. Sufficient...
Given a fixed set S of n keys, we would like to store them so that queries of the form "Is x ∈ S?" can be answered quickly. A commonly employed scheme to solve this problem uses a table to store the keys, and a special purpose program depending on S which probes the table. We analyze the tradeoff between the maximum number of probes allowable to answer a query, and the information-theoretic...
A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence...
We consider uniform circuit complexity, introduced by Borodin as a model of parallel complexity. Three main results are presented. First, we show that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Second, we apply this to characterize the class of polynomial size and...
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