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 ...

A tree functional is called additive if it satisfies a recursion of the form F (T ) = ∑k j=1 F (Bj)+f(T ), where B1, . . . , Bk are the branches of the tree T and f(T ) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalised planeoriented increasin...

Recently, Stanley [Longest alternating subsequences of permutations, preprint, arXiv/0511419v1] studied the length of the longest alternating subsequence of a permutation in the symmetric group,where a sequencea, b, c, d, . . . isalternating ifa >bd < · · ·. In this paper, we extend this result to the case of k-ary words. More precisely, we find an explicit formula for the generating functio...

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...