2,729 research outputs found
Words in Linear Groups, Random Walks, Automata and P-Recursiveness
Fix a finite set . Denote by the number
of products of matrices in of length that are equal to 1. We show that
the sequence is not always P-recursive. This answers a question of
Kontsevich.Comment: 10 pages, 1 figur
EERTREE: An Efficient Data Structure for Processing Palindromes in Strings
We propose a new linear-size data structure which provides a fast access to
all palindromic substrings of a string or a set of strings. This structure
inherits some ideas from the construction of both the suffix trie and suffix
tree. Using this structure, we present simple and efficient solutions for a
number of problems involving palindromes.Comment: 21 pages, 2 figures. Accepted to IWOCA 201
Symbolic stochastic dynamical systems viewed as binary N-step Markov chains
A theory of systems with long-range correlations based on the consideration
of binary N-step Markov chains is developed. In the model, the conditional
probability that the i-th symbol in the chain equals zero (or unity) is a
linear function of the number of unities among the preceding N symbols. The
correlation and distribution functions as well as the variance of number of
symbols in the words of arbitrary length L are obtained analytically and
numerically. A self-similarity of the studied stochastic process is revealed
and the similarity group transformation of the chain parameters is presented.
The diffusion Fokker-Planck equation governing the distribution function of the
L-words is explored. If the persistent correlations are not extremely strong,
the distribution function is shown to be the Gaussian with the variance being
nonlinearly dependent on L. The applicability of the developed theory to the
coarse-grained written and DNA texts is discussed.Comment: 14 pages, 13 figure
Skewincidence
We introduce a new class of problems lying halfway between questions about
graph capacity and intersection. We say that two binary sequences x and y of
the same length have a skewincidence if there is a coordinate i for which
x_i=y_{i+1}=1 or vice versa. We give rather sharp bounds on the maximum number
of binary sequences of length n any pair of which has a skewincidence
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