Related papers: Efficient Algorithm for the Linear Complexity of S…
We present the first linear time algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working space. A simpler variant of this algorithm computes the plain ($n\lg n$-bit)…
The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…
We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the…
Graph games with {\omega}-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the…
A key requirement in sequence to sequence processing is the modeling of long range dependencies. To this end, a vast majority of the state-of-the-art models use attention mechanism which is of O($n^2$) complexity that leads to slow…
Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…
We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital…
We propose a low-complexity sign-dependent metric for sequence selection and study the nonlinear shaping gain achievable for a given computational cost, establishing a benchmark for future research. Small gains are obtained with feasible…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a…
A linear time algorithm to find a set of nearest elements in a mesh.
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
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 framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…