Related papers: Word equations in linear space
We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…
Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…
The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…
The compression is an important topic in computer science which allows we to storage more amount of data on our data storage. There are several techniques to compress any file. In this manuscript will be described the most important…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
Reliable evaluation protocols are of utmost importance for reproducible NLP research. In this work, we show that sometimes neither metric nor conventional human evaluation is sufficient to draw conclusions about system performance. Using…
Large Language Models (LLMs) excel at various tasks, including problem-solving and question-answering. However, LLMs often find Math Word Problems (MWPs) challenging because solving them requires a range of reasoning and mathematical…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given…
In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. In the context of regression problems, there has been enormous amount of effort to recover an unknown…
In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class $L_k$ if it is a subset of the catenation of $k$ languages…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Kinetic models of biochemical systems used in the modern literature often contain hundreds or even thousands of variables. While these models are convenient for detailed simulations, their size is often an obstacle to deriving mechanistic…
We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that…
Word embedding techniques heavily rely on the abundance of training data for individual words. Given the Zipfian distribution of words in natural language texts, a large number of words do not usually appear frequently or at all in the…
The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary,…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
A topological argument is presented concering the structure of semantic space, based on the negative correlation between polysemy and word length. The resulting graph structure is applied to the modeling of free-recall experiments,…