Related papers: On arch factorization and subword universality for…
A popular approach to sentence compression is to formulate the task as a constrained optimization problem and solve it with integer linear programming (ILP) tools. Unfortunately, dependence on ILP may make the compressor prohibitively slow,…
The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all…
A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] , \dots w[i_{|u|}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq |w|$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if every word…
In this paper we present an application of a simple technique of local recompression, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations. The technique is…
We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such…
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
We introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products or inverses. This factorization is a critical part of a…
Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
Since the amount of information on the internet is growing rapidly, it is not easy for a user to find relevant information for his/her query. To tackle this issue, much attention has been paid to Automatic Document Summarization. The key…
This paper presents a unified matrix factorization framework for classical and robust clustering. We begin by revisiting the well-known equivalence between crisp k-means clustering and matrix factorization, following and rigorously…
How can we compress language models without sacrificing accuracy? The number of compression algorithms for language models is rapidly growing to benefit from remarkable advances of recent language models without side effects due to the…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
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…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Many large-scale Web applications that require ranked top-k retrieval such as Web search and online advertising are implemented using inverted indices. An inverted index represents a sparse term-document matrix, where non-zero elements…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…