This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong. With the new shift sequences, some new families of p-ary sequences with desired properties can be obtained. A lower bound on the number of new families of binary sequences is also established.

in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

When analyzing a large amount of data, analysts often define groups over data elements that share certain properties. Using these groups as the unit of analysis not only reduces the data volume, but also allows detecting various patterns in the data. This involves analyzing intersection relations between these groups, and how the element attributes vary between these intersections. This kind of...

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occurring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1, . . . , N} has |A| 8000 log N/ log log N for sufficiently large N. The proof combines results from extremal graph theory with numbe...

Automata over infinite words provide a powerful framework, which we can use to solve various decision problems. However, the automatized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Büchi automata, which recognize the ω-regular languages in the Borel class Fσ ∩Gδ, can be handled algorithmically almost as ...

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map fr...

We present here a view on abstraction based on the relation between sentences in a partially ordered language L and truth values of these sentences on a set of instances W . In Formal Concept Analysis, this relation is materialized as a lattice denoted as G that relates L and the powerset P(W )). We show here that projections on a lattice (here either L or the powerset P(W )) that are known to ...

Discrete systems such as sets, monoids, groups are familiar categories. The internal strucutre of the latter two is defined by an algebraic operator. In this paper we describe the internal structure of the base set by a closure operator. We illustrate the role of such closure in convex geometries and partially ordered sets and thus suggest the wide applicability of closure systems. Next we deve...

Besides all the attention given to lattice constructions, it is common to find some very interesting nonlattice constellations, as Construction C, for example, which also has relevant applications in communication problems (multi-level coding, multi-stage decoding, good quantization efficieny). In this work we present a constellation which is a subset of Construction C, based on inter-level cod...