Related papers: Record values in appending and prepending bitstrin…
We prove a relationship between certain integer expressions involving operators similar to the binary exclusive or. This gives a proof and generalization of a result conjectured about sequence A178729 in Sloane's Online Encyclopedia of…
In this paper, we describe minimal string attractors of prefixes of simple Parry sequences. These sequences form a coding of distances between consecutive $\beta$-integers in numeration systems with a real base $\beta$. Simple Parry…
A sequence of non-negative integers is called a B_k sequence if all the sums of arbitrary k elements are different. In this paper, we will present a new estimation for the upper bound of B_k sequences.
We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the…
In this paper we examine two ways of coding sequences in arithmetical theories. We investigate under what conditions they work. To be more precise, we study the creation of objects of a data-type that we call ur-strings, roughly sequences…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Using the classic two's complement notation of signed integers, the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. We introduce a Fibonacci-equivalent of…
A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…
We describe the results of the computation of aliquot sequences with small starting values. In particular all sequences with starting values less than a million have been computed until either termination occurred (at 1 or a cycle), or an…
A pairing function for the non-negative integers is said to be binary perfect if the binary representation of the output is of length 2k or less whenever each input has length k or less. Pairing functions with square shells, such as the…
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of…
We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base $\beta$ in $\mathbb{C}$ and a finite digit set $\mathcal{A}$ of contiguous integers containing $0$. For a…
This note discusses the existence of prime numbers in short intervals. An unconditional elementary argument seems to prove the existence of primes in the short intervals [x, x + y], where y >= x^(1/2)(log x)^e, e > 0, and a sufficiently…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…
In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the…
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit (BSD) representation of integers is used widely in efficient computation, coding theory and other…
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump…