Discrete Mathematics and Applications

doi: 10.1515/dma-2014-frontmatter3pmid: N/A

Bauman, Konstantin E.

doi: 10.1515/dma-2014-0012pmid: N/A

Abstract We prove that the square-to-linear ratio of a regular Peano curve that maps the unit interval onto the unit square is at least five.

Bukhman, Anton V.

doi: 10.1515/dma-2014-0013pmid: N/A

Abstract The algorithmic complexity of periodicity detection of Boolean functions given in a polynomial form is investigated. A function is said to be periodic with period ó if it takes the same values on input strings which differ only by inverting the components corresponding to nonzero entries in the bit string ó. Two polynomial-time algorithms for checking whether a given bit string is a period of a given Boolean function are presented. The relationship between the periods of a function and the length of its polynomial is investigated. The problem of finding the periods is explicitly reduced in polynomial time to the problem of solving a system of Boolean equations.

Dergach, Petr S.

doi: 10.1515/dma-2014-0014pmid: N/A

Abstract The goal of the paper is to prove that the problem of uniqueness of alphabetical decoding of ø- regular languages is decidable

Petushko, Alexandr A.

doi: 10.1515/dma-2014-0015pmid: N/A

Abstract We consider formal languages that are defined by matrices of bigram frequences. These languages were studied by the author on the qualitative level in the paper "‘On bigramlanguages"`.Here the connections between language cardinality and initial bigram frequency matrix are investigated and asymptotic estimates of language cardinalities and of fractions of numbers of bigram frequency matrices with various properties are presented

Pogorelov, Boris A.; Pudovkina, Marina A.

doi: 10.1515/dma-2014-0016pmid: N/A

Abstract The Hamming distance from permutations of degree n = wr to the union of all groups Sw Õ Sr with given parameters w, r and to the union of all such groups with arbitrary nontrivial parameters w, r is investigated. The values of the distance from the known s-boxes to some wreath products are presented.

Rybakov, Alexander S.

doi: 10.1515/dma-2014-0017pmid: N/A

Abstract An upper estimate for the norm of some positive integer solution of an arbitrary system of linear homogeneous equations with integer coefficients with nonempty set of positive integer solutions is obtained. This estimate is used to estimate from above the norm of a vector in which the components are powers of binomialswhose product is a difference polynomial of minimal possibleweight. The last result can be applied in the theory of beam steerable antenna arrays