Separation of two-query-adaptive from two-query-non-adaptive completeness if NP is not small

Under the hypothesis that NP does not have p-measure O (roughly, that NP contains more than a negligible subset of exponential time), it is shown that there is a language that is ≤ P/2-T complete but not ≤ P/2-tt complete for NP. This conclusion, widely believed to be true, is not known to follow from P ≠ NP or other traditional complexity-theoretic hypotheses. This is a very preliminar version

Pushdown Compression

The pressing need for eficient compression schemes for XML documents has recently been focused on stack computation [6, 9], and in particular calls for a formulation of information-lossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms. In this paper we introduce the model of pushdown compressor, based on pushdown transducers that compute a single injective function while keeping the widest generality regarding stack computation. The celebrated Lempel-Ziv algorithm LZ78 [10] was introduced as a general purpose compression algorithm that outperforms finite-state compressors on all sequences. We compare the performance of the Lempel-Ziv algorithm with that of the pushdown compressors, or compression algorithms that can be implemented with a pushdown transducer. This comparison is made without any a priori assumption on the data's source and considering the asymptotic compression ratio for infinite sequences. We prove that Lempel-Ziv is incomparable with pushdown compressors

ALMOST-R: characterizations using different concepts of randomness

We study here the classes of the form ALMOST-R, for R a reducibility. This includes among other the classes BPP, P and PH. We give a characterization of this classes in terms of reducibility to n-random languages, a subclass of algorithmically random languages. We also give a characterization of classes of the form ALMOST-R in terms of resource bounded measure, for R reducibility of a restricted kind

Computing absolutely normal numbers in nearly linear time

A real number x is absolutely normal if, for every base b ≥ 2, every two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion of x. This paper presents an explicit algorithm that generates the binary expansion of an absolutely normal number x, with the nth bit of x appearing after npolylog(n) computation steps. This speed is achieved by simultaneously computing and diagonalizing against a martingale that incorporates Lempel-Ziv parsing algorithms in all bases