Related papers: Linear Shift-Register Synthesis for Multiple Seque…
In this paper, a new approach for decoding low-rate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shift-register…
We show how to solve a generalised version of the Multi-sequence Linear Feedback Shift-Register (MLFSR) problem using minimisation of free modules over $\mathbb F[x]$. We show how two existing algorithms for minimising such modules run…
An algorithm for constructing a shortest binary k-stage machine generating a given binary sequence is presented. This algorithm can be considered as an extension of Berlekamp-Massey algorithm to the non-linear case.
The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for…
The Berlekamp--Massey--Sakata algorithm and the Scalar-FGLM algorithm both compute the ideal of relations of a multidimensional linear recurrent sequence.Whenever quering a single sequence element is prohibitive, the bottleneck of these…
Many constraints restricting the result of some computations over an integer sequence can be compactly represented by register automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising…
The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
We compare thoroughly the Berlekamp -- Massey -- Sakata algorithm and the Scalar-FGLM algorithm, which compute both the ideal of relations of a multi-dimensional linear recurrent sequence. Suprisingly, their behaviors differ. We detail in…
Binary machines are a generalization of Feedback Shift Registers (FSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the register stages is required. In this paper, we present an algorithm…
We develop a new algorithm to compute determinants of all possible Hankel matrices made up from a given finite length sequence over a finite field. Our algorithm fits within the dynamic programming paradigm by exploiting new recursive…
The longest common subsequence (LCS) is a fundamental problem in string processing which has numerous algorithmic studies, extensions, and applications. A sequence $u_1, \ldots, u_f$ of $f$ strings s said to be an ($f$-)segmentation of a…
For a finite state automaton, a synchronizing sequence is an input sequence that takes all the states to the same state. Checking the existence of a synchronizing sequence and finding a synchronizing sequence, if one exists, can be…
Software engineers mainly write code by editing existing programs. In contrast, language models (LMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of sequential edit data. While…
Multiple sequence alignment (MSA) has been one of the most important problems in bioinformatics for more decades and it is still heavily examined by many mathematicians and biologists. However, mostly because of the practical motivation of…
We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…
The advent of "next-generation" DNA sequencing (NGS) technologies has meant that collections of hundreds of millions of DNA sequences are now commonplace in bioinformatics. Knowing the longest common prefix array (LCP) of such a collection…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
Multi-sequence MRI is valuable in clinical settings for reliable diagnosis and treatment prognosis, but some sequences may be unusable or missing for various reasons. To address this issue, MRI synthesis is a potential solution. Recent deep…
Transformer-based sequence-to-sequence architectures, while achieving state-of-the-art results on a large number of NLP tasks, can still suffer from overfitting during training. In practice, this is usually countered either by applying…