Geodesic

Sommaire du Fascicule no. 1

Conjugacy word problem in the tree product of free groups with a cyclic amalgamation
p. 3-18
Steganographic capacity for one-dimensional Markov cover} \runningtitle{Steganographic capacity for one-dimensional Markov cover} \author*[1]{Valeriy A. Voloshko} \runningauthor{V.\,A. Voloshko} \affil[1]{ Belarusian State University, e-mail: valeravoloshko@yandex.ru} \abstract{For shift-invariant probability measures on the set of infinite two-sided binary sequences (one-dimensional covers) we introduce the notion of capacity as a maximum portion of embedded into the cover uniformly distributed (purely random) binary sequence (message) that admits special correction of the cover restoring its distribution up to distribution of $n$-tuples (subwords of some fixed length $n$). ``Special correction'' is carried out using the proposed new algorithm that changes some of the cover's symbols not occupied by embedded message. The features of the introduced capacity are examined for the Markov cover. In particular, we show how capacity may be significantly increased by weakening of the standard constraint that positions for message embedding have to be chosen by independent unfair coin tosses. Experimental results are presented for correction of real steganographic covers after LSB-embedding.} \keywords{binary sequence, shift-invariant measure, steganography, capacity
p. 19-43
Independent sets in graphs
p. 44-77
Successive partition of edges of bipartite graph into matchings
p. 78-86
Tests of contact closure for contact circuits
p. 87-100
Application of Hadamard product to some combinatorial and probabilistic problems
p. 101-112
On asymptotics of branching processes with immigration
p. 113-122
The second coordinate sequence of the MP-LRS over nontrivial Galois ring of an odd characteristic
p. 123-149
Extension of the Rissanen algorithm to the factorization of block-Hankel matrices for solving systems of linear equations
p. 150-155

Sommaire du Fascicule no. 2

The algorithm for identical object searching with bounded worst-case complexity and linear memory
p. 3-11
On the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates
p. 12-26
Estimating the number of solutions of systems of nonlinear equations with linear recurring arguments by the spectral method
p. 27-43
Complexity classification of the edge coloring problem for a~family of graph classes
p. 44-50
On FE-precomplete classes in countable-valued logic
p. 51-57
On limit behavior of maximum vertex degree in a conditional configuration graph near critical points
p. 58-70
Estimates of the number of $(k,l)$-sumsets in the finite Abelian group
p. 71-80
On the number of functions of $k$-valued logic which are polynomials modulo composite $k$
p. 81-91
Limit theorems for the number of successes in random binary sequences with random embeddings
p. 92-107
Upper bounds for the size and the depth of formulae for MOD-functions
p. 108-116
On $1$-stable perfectly balanced Boolean functions
p. 117-126
On bases of closed classes of vector functions of many-valued logic
p. 127-132
Bezout rings without non-central idempotents
p. 133-145
Bounds for the average-case complexity of monotone Boolean functions
p. 146-153
Modular algorithm for reducing matrices to the Smith normal form
p. 154-160

Sommaire du Fascicule no. 3

Functional limit theorem for a stopped random walk attaining a high level
p. 3-13
Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
p. 14-25
On the number of labeled outerplanar $k$-cycle blocks
p. 26-27
Large deviations of branching processes with immigration in random environment
p. 28-48
Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process
p. 49-58
Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle
p. 59-96
On the probability of existence of substrings with the same structure in a random sequence
p. 97-110
Cardinality of subsets of the residue group with nonunit differences of elements
p. 111-125
Independence numbers of random sparse hypergraphs
p. 126-144
Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
p. 145-159

Sommaire du Fascicule no. 4

Валентин Федорович Колчин (1934--2016)
p. 3-5
On the non-recurrent random walk in a random environment
p. 6-28
Lower bound for the complexity of five-valued polarized polynomials
p. 29-37
The cross-correlation function of complications of linear recurrent sequences
p. 38-49
Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
p. 50-57
Reduced multitype critical branching processes in random environment
p. 58-79
The minimum number of negations in circuits for systems of multi-valued functions
p. 80-90
Bounded prefix concatenation operation and finite bases with respect to the superposition
p. 91-99
On groups containing the additive group of the residue ring or the vector space
p. 100-121
On the number of subsets of the residue ring such that the difference of any pair of elements is not invertible
p. 122-138
On the number of maximal independent sets in complete $q$-ary trees
p. 139-149
On serial rings
p. 150-157