Related papers: On Searching Zimin Patterns
Consider an independent site percolation model on $\Z^d$, with parameter $p \in (0,1)$, where all long range connections in the axes directions are allowed. In this work we show that given any parameter $p$, there exists and integer $K(p)$…
Search engines perform the task of retrieving information related to the user-supplied query words. This task has two parts; one is finding "featured words" which describe an article best and the other is finding a match among these words…
Motivated by the study of Fibonacci-like Wang shifts, we define a numeration system for $\mathbb{Z}$ and $\mathbb{Z}^2$ based on the binary alphabet $\{0,1\}$. We introduce a set of 16 Wang tiles that admits a valid tiling of the plane…
In this paper, we study pattern matching in the set F_{n,k} of fillings of the k x n rectangle with the integers 1,...,kn such that the elements in any column increase from bottom to top. Let P be a column strict tableau of shape 2^k. We…
The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…
In an effort to better understand meaning from natural language texts, we explore methods aimed at organizing lexical objects into contexts. A number of these methods for organization fall into a family defined by word ordering. Unlike…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pattern avoiding permutations is adapted to words. As an…
We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An…
This paper presents a novel approach to Chinese characters through the lens of physics, network analysis, and natural systems. Computational analysis of over 6,000 characters identified 422 elemental characters as fundamental building…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
We consider the Min-$r$-Lin$(Z_m)$ problem: given a system $S$ of length-$r$ linear equations modulo $m$, find $Z \subseteq S$ of minimum cardinality such that $S-Z$ is satisfiable. The problem is NP-hard and UGC-hard to approximate in…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern…