We classify a type of language called a reflectable language. We then develop a generic algorithm that can be used to list all strings of length n for any reflectable language in Gray code order. The algorithm generalizes Gray code algorithms developed independently for k-ary strings, restricted growth strings, and k-ary trees, as each of these objects can be represented by a reflectable langua...

In this paper, we suggest a new technique to create index helping for querying almost identical similarities with keywords in case there is no correct match found. It’s based on a signature graph and n-ary tree helping to query related information when there is no correct match. Main idea is a signature graph structure, created based on signature file, created for a layer and signature files ar...

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup Q is (permutably) reducible if Q(x1, . . . , xn) = P ( R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ) where P and R are (n−k+1)-ary and k-ary quasigroups, σ is a permutation, a...

We consider the problem of solving equations over k-ary trees. Here an equation is a pair of labeled-ary trees, where is a function associating an arity to each label. A solution to an equation is a morphism from-ary trees to k-ary trees that maps the left and right hand side of the equation to the same k-ary tree. This problem is a generalization of the word uniication problem posed by A. Mark...

We characterize the set of all n-ary quasigroups of order 4: every n-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an n-ary quasigroup can be represented as a composition of k-ary and (n− k +1)-ary quasigroups for some k from 2 to n−1, where the order of arguments in the representation can differ from the original order. The set of semilinea...

The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

This article investigates the problem of designing virtual di-paths (VPs) in a directed ATM model, in which the ow of information in the two directions of a link are not identical. On top of a given physical network we construct directed VPs. Routing in the physical network is done using these VPs. Given the capacity of each physical link (the maximum number of VPs that can pass through the lin...

In Bevan et al. (2016), the study of patterns in forests of binary shrubs was introduced. A k-ary heap H is a k-ary tree labeled with {1, . . . , n} such that every child has a larger label than its parent. Given a k-ary heap H , we associate a permutation σH with H by recording the vertex labels as they are encountered in the breadth-first search of the tree. For example, in Figure 1, we pictu...

In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. We show that the splicing algebras are an n-ary envelope for algebras of DNA recombinati...