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For every total recursive time bound $t$, a constant fraction of all compressible (low Kolmogorov complexity) strings is $t$-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length $n$ is compressible to $log n$ yet $t$-bounded incompressible below ${1/4}n - log n$; and there are countable infinitely many recursive infinite sequence of which every initial segment is similarly $t$-bounded incompressible. These results are related to, but different from, Barzdinss lemma.
This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [Allender et al] to settle this conje
Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on disjointness in the m
The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to ca
Two parties wish to carry out certain distributed computational tasks, and they are given access to a source of correlated random bits. It allows the parties to act in a correlated manner, which can be quite useful. But what happens if the shared ran
In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $rho$ drawn from a known ensemble (but without knowing what $rho$ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a n