Related papers: Notes on properties of binary strings which encode…
The genome rearrangement problem computes the minimum number of operations that are required to sort all elements of a permutation. A block-interchange operation exchanges two blocks of a permutation which are not necessarily adjacent and…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
The binary signed-digit representation of integers is used for efficient computation in various settings. The Stern polynomial is a polynomial extension of the well-studied Stern diatomic sequence, and has itself has been investigated in…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
We study a recursively defined sequence which is constructed using the least common multiple. It has been conjectured that every term of that sequence is $1$ or a prime. In this paper we show that this claim is connected to a strong version…
In this paper we present the experimental results that more clearly than any theory suggest an answer to the question: when in detection of large (probably) prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or, to…
The signed-bit representation of real numbers is like the binary representation, but in addition to 0 and 1 you can also use -1. It lends itself especially well to the constructive (intuitionistic) theory of the real numbers. The first part…
The binomial notation (w u) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (w ab) and (w ba) when a and b are distinct letters.…
A novel notion of unpredictable strings is revealed and utilized to define deterministic unpredictable sequences on a finite number of symbols. We prove the first law of large strings for random processes in discrete time, which confirms…
The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
Let $S$ be a string of $l$ decimal digits. We give an explicit upper bound on some prime $p$ whose decimal representation contains the string $S$. We also show, as a corollary of the Green-Tao theorem, that there are arbitrarily long…
Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…
Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…
It is shown that the multiplicity distribution associated to self-shadowing events satisfies an universal equation in terms of the minimum bias distribution. The number of elementary collisions, basic in the structure of any multiple…
Prime numbers, whose properties are important subjects in mathematics, are also fundamental in computer science notably in IT security, Cryptocurrencies as Bitcoin and Blockchain, cryptography, Code theory notably Error detection codes,…