Related papers: Parikh matrices and Parikh Rewriting Systems
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of…
Kan extensions provide a natural general framework for a variety of combinatorial problems. We have developed rewriting procedures for Kan extensions (over the category of sets) and this enables one program to address a wide range of…
Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
Given a text and a pattern over two types of symbols called constants and variables, the parameterized pattern matching problem is to find all occurrences of substrings of the text that the pattern matches by substituting a variable in the…
We study permutation (jumbled/Abelian) pattern matching over a general alphabet $\Sigma$. Given a pattern P of length m and a text T of length n, the classical task is to decide whether T contains a length-m substring whose Parikh vector…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
The trust region subproblem with a fixed number m additional linear inequality constraints, denoted by (Tm), have drawn much attention recently. The question as to whether Problem (Tm) is in Class P or Class NP remains open. So far, the…
This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact…
Matrix and tensor completion are frameworks for a wide range of problems, including collaborative filtering, missing data, and image reconstruction. Missing entries are estimated by leveraging an assumption that the matrix or tensor is…
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral…
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…
In light of recent hardware advances, it is striking that real arithmetic in balanced ternary logic has received almost no attention in the literature. This is particularly surprising given ternary logic's promising properties, which could…
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
We introduce semaphore codes associated to a Turing machine via resets. Semaphore codes provide an approximation theory for resets. In this paper we generalize the set-up of our previous paper "Random walks on semaphore codes and delay de…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…