相关论文: The complexity of normal form rewrite sequences fo…

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…

The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…

The size $b$ of the smallest bidirectional macro scheme, which is arguably the most general copy-paste scheme to generate a given sequence, is considered to be the strictest reachable measure of repetitiveness. It is strictly lower-bounded…

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized…

For a word $S$, let $f(S)$ be the largest integer $m$ such that there are two disjoints identical (scattered) subwords of length $m$. Let $f(n, \Sigma) = \min \{f(S): S \text{is of length} n, \text{over alphabet} \Sigma \}$. Here, it is…

The combined universal probability M(D) of strings x in sets D is close to max_{x \in D} M({x}): their ~ logs differ by at most D's information j = I(D:H) about the halting sequence H. Thus if all x have complexity K(x) > k, D carries > i…

The expected length of longest common subsequences is a problem that has been in the literature for at least twenty five years. Determining the limiting constants \gamma_k appears to be quite difficult, and the current best bounds leave…

The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…

The study of Armstrong codes is motivated by the problem of understanding complexities of dependencies in relational database systems, where attributes have bounded domains. A $(q,k,n)$-Armstrong code is a $q$-ary code of length $n$ with…

We present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In…

This paper argues that the judicial use of formal language theory and grammatical inference are invaluable tools in understanding how deep neural networks can and cannot represent and learn long-term dependencies in temporal sequences.…

The (Mahler-Popken) complexity $\| n \|$ of a natural number $n$ is the smallest number of ones that can be used via combinations of multiplication and addition to express $n$, with parentheses arranged in such a way so as to form legal…

We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This…

Specificity is important for extracting collocations, keyphrases, multi-word and index terms [Newman et al. 2012]. It is also useful for tagging, ontology construction [Ryu and Choi 2006], and automatic summarization of documents [Louis and…

We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…

A nearly linear recurrence sequence (nlrs) is a complex sequence $(a_n)$ with the property that there exist complex numbers $A_0$,$\ldots$, $A_{d-1}$ such that the sequence $\big(a_{n+d}+A_{d-1}a_{n+d-1}+\cdots +A_0a_n\big)_{n=0}^{\infty}$…

In this paper we give a criterion by which one can conclude that every reduction of a basic term to normal form has the same length. As a consequence, the number of steps to reach the normal form is independent of the chosen strategy. In…

Document listing on string collections is the task of finding all documents where a pattern appears. It is regarded as the most fundamental document retrieval problem, and is useful in various applications. Many of the fastest-growing…