Satisfiability of word equations problem is: Given two sequences consisting letters and variables decide whether there is a substitution for the that turns this equation into true equality. The exact computational complexity remains unknown, with best lower upper bounds being, respectively, NP PSPACE . Recently, novel technique recompression was applied to problem, simplifying known proofs lowe...

Abstract Linear local tangent space alignment (LLTSA) is a classical dimensionality reduction method based on manifold. However, LLTSA and all its variants only consider the one-way mapping from high-dimensional to low-dimensional space. The projected data may not accurately effectively “represent” original samples. This paper proposes novel linear autoencoder called LLTSA-AE (LLTSA with Autoen...

Local linear prediction is one of several methods that have been applied to prediction of real time series including financial time series. The difference from global linear prediction is that, for every single point prediction, a different linear autoregressive (AR) model is estimated based only on a number of selected past scalar data segments. Geometrically, these data segments correspond to...

We present a randomized algorithm sorting n integers in O(n p log logn) expected time and linear space. This improves the previous O(n log logn) bound by Anderson et al. from STOC’95. As an immediate consequence, if the integers are bounded by U , we can sort them in O(n p log logU) expected time. This is the first improvement over the O(n log logU) bound obtained with van Emde Boas’ data struc...

We show that any randomized algorithm that runs in space S and time T and uses poly(S) random bits can be simulated using only O(S) random bits in space S and time T + poly(S). A deterministic simulation in space S follows. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.

We introduce a new parallel algorithm for pairwise sequence alignment, called Parallel FastLSA, that finds optimal answers, uses linear space with respect to problem size and number of processors, and achieves good speedups in practice. Computational biologists use sequence alignment algorithms to compare sequences of DNA (or proteins). Since the sequences can be long, space efficiency and turn...

When a switched linear system is not completely controllable, the controllability subspace is not enough to describe the controllability of the system over whole state space. In this case the state space can be divided into two or three control-invariant sub-manifolds, which form a control-related partition of the state space. This paper investigates when each component is a controllable sub-ma...