Related papers: Parikh Matrices and Strong M-Equivalence
Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a given size of an infinite sequence. How practical is this…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.
A real $n$-by-$n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein characterize the triples: size, constant, and rank for which…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
Indexed languages are a classical notion in formal language theory. As the language equivalent of second-order pushdown automata, they have received considerable attention in higher-order model checking. Unfortunately, counting properties…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…
Cross-Language Information Retrieval (CLIR) and machine translation (MT) resources, such as dictionaries and parallel corpora, are scarce and hard to come by for special domains. Besides, these resources are just limited to a few languages,…
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and…
Various variants of Parikh automata on infinite words have recently been introduced in the literature. However, with some exceptions only their non-deterministic versions have been considered. In this paper we study the deterministic…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
The paper studies algebraic strong shift equivalence of matrices over $n$-variable polynomial rings over a principal ideal domain $D$($n\leq 2$). It is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full rank…
LPMLN is a powerful knowledge representation and reasoning tool that combines the non-monotonic reasoning ability of Answer Set Programming (ASP) and the probabilistic reasoning ability of Markov Logic Networks (MLN). In this paper, we…
We introduce the notion of $\imath$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke…