This paper focuses on multi-ary α-semantic resolution automated reasoning method based on multi-ary α-resolution principle for lattice-valued propositional logic LP(X) with truth-value in lattice implication algebras. The definitions of the multi-ary α-semantic resolution and multi-ary α-semantic resolution deduction in lattice-valued propositional logic LP(X) are given, respectively, and the s...

n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergr...

a parallel algorithm for generating t-ary tree sequences in reverse b-order is presented. the algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time o(1). the algorithm is executed on a crew sm simd model, and is adaptive and cost-optimal. prior to the discussion of the parallel algorithm a new sequential generation with o(1) average time ...

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...

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...

Fuzzy n-ary hypergroups were introduced as suitable generalizations of fuzzy polygroups and a special case of fuzzy n-ary hyper groups. The aim of this paper is to introduce the notion of fuzzy n-ary factor polygroups of a polygroup. Based on the fuzzy n-ary factor group, we also study the product structures of the generating fuzzy factor n-ary groups. At the end of the paper, we prove the fund...

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...

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...