This paper is devoted to the generation and evaluation of the Chaos-based M-ary spreading sequences on communications systems. Sequences obtained by repeating a truncated and multi-ary quantized chaotic series are compared with classical m-sequences by means of the autocorrelation and cross-correlation properties and power-spectral features. Anti-noise performance of binary sequences and chaoti...

Discovering new integer sequences and generalizing the existing ones are important and of great interest. In this article, various balanced k-ary trees are first studied and their taxonomy is built. In particular, two systematic balanced k-ary trees, whose nth tree is determined by a certain algorithm, are identified, i.e., complete and sizebalanced k-ary trees. The integer sequences from the f...

In this paper the phase transition, that is to say the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solution as the constraints become tighter, is investigated by examining n-ary Constraint Satisfaction Problems (CSPs). The paper reports a series of experiments with samples of randomly-generated problems, using a fami...

In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k...

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we solve two open problems related to them raised in Phys. Rev. Lett. 117, 150401 (2016). We first show that fundamentally bina...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

One of the most important problems in the sequence design is to find sequences with good correlation properties. Recently, expect for the binary Pseudo-Random Sequences (PRSs), much progress has been obtained for ternary and p-ary PRSs. In this paper a short survey of p-ary PRSs and their properties is made. As a result their classification is suggested without claiming its full completeness.

Fuzzy rough n-ary subhypergroups are introduced and characterized.

q–ary codes capable of correcting all unidirectional errors of certain level 1 ≤ l ≤ q − 2 are considered. We also discuss some related extremal combinatorial problems.