Node selection in trees is a fundamental operation to XML databases, programming languages, and information extraction. We propose a new class of querying languages to define n-ary node selection queries as compositions of monadic queries. The choice of the underlying monadic querying language is parametric. We show that compositions of monadic MSO-definable queries capture n-ary MSO-definable ...

This article investigates numerous integer sequences derived from two special balanced k-ary trees. Main contributions of this article are two fold. The first one is building a taxonomy of various balanced trees. The other pertains to discovering new integer sequences and generalizing existing integer sequences to balanced k-ary trees. The generalized integer sequence formulae for the sum of he...

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...

The group Am of automophisms of a one-rooted m-ary tree admits a diagonal monomorphism which we denote by x. Let A be an abelian state-closed (or self-similar) subgroup of Am. We prove that the recurrence and tree-topological closure A∗ of A is additively a finitely presented Zm [[x]]module where Zm is the ring of m-adic integers. Moreover, if A∗ is torsion-free then it is a finitely generated ...

A k-ary de Bruijn sequence of order n is a cyclic sequence of length k in which each k-ary string of length n appears exactly once as a substring. A shift rule for a de Bruijn sequence of order n is a function that maps each length n substring to the next length n substring in the sequence. We present the first known shift rule for k-ary de Bruijn sequences that runs in O(1)-amortized time per ...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

Constraint satisfaction problem (CSP) paradigm has proved highly successful for solving product configuration problems, particularly for build-to-order configuration in determining combination of different predefined component types. However, many real world customized products deal with engineer-to-order configuration, where product configuration is generated not only from combinations of diff...