Related papers: Testing Suffixient Sets
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at…
Text mining is about looking for patterns in natural language text, and may be defined as the process of analyzing text to extract information from it for particular purposes. In previous work, we claimed that compression is a key…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…
Conformal prediction is a statistical framework that generates prediction sets containing ground-truth labels with a desired coverage guarantee. The predicted probabilities produced by machine learning models are generally miscalibrated,…
We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
The well-known dictionary-based algorithms of the Lempel-Ziv (LZ) 77 family are the basis of several universal lossless compression techniques. These algorithms are asymmetric regarding encoding/decoding time and memory requirements, with…
Cadences are structurally maximal arithmetic progressions of indices corresponding to equal characters in an underlying string. This paper provides a polynomial time detection algorithm for 3-cadences in grammar-compressed binary strings.…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
Indexing a set of strings for prefix search or membership queries is a fundamental task with many applications such as information retrieval or database systems. A classic abstract data type for modelling such an index is a trie. Due to the…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
We propose a new indexing structure for parameterized strings, called parameterized position heap. Parameterized position heap is applicable for parameterized pattern matching problem, where the pattern matches a substring of the text if…
Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their…
The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…
When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main…
Sequence tagging models for constituent parsing are faster, but less accurate than other types of parsers. In this work, we address the following weaknesses of such constituent parsers: (a) high error rates around closing brackets of long…