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In this paper, we investigate the detection problem of binary faster-than-Nyquist (FTN) signaling and propose a novel sequence estimation technique that exploits its special structure. In particular, the proposed sequence estimation…

Various adaptive abilities are required for robots interacting with humans in daily life. It is difficult to design adaptive algorithms manually; however, by using end-to-end machine learning, labor can be saved during the design process.…

The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. However, the merit factor problem is…

We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation.

Registers with Non-Linear Update (RNLUs) are a generalization of Non-Linear Feedback Shift Registers (NLFSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the stages is required. In this…

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…

In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$…

A framework is proposed for the unconditional generation of synthetic time series based on learning from a single sample in low-data regime case. The framework aims at capturing the distribution of patches in wavelet scalogram of time…

The problem of sequentially finding an independent and identically distributed (i.i.d.) sequence that is drawn from a probability distribution $f_1$ by searching over multiple sequences, some of which are drawn from $f_1$ and the others of…

We consider the problem of lossless compression of individual sequences using finite-state (FS) machines, from the perspective of the best achievable empirical cumulant generating function (CGF) of the code length, i.e., the normalized…

A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…

We introduce Mini-Sequence Transformer (MsT), a simple and effective methodology for highly efficient and accurate LLM training with extremely long sequences. MsT partitions input sequences and iteratively processes mini-sequences to reduce…

Labeled handwriting data is often scarce, limiting the effectiveness of recognition systems that require diverse, style-consistent training samples. Handwriting synthesis offers a promising solution by generating artificial data to augment…

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…

In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a constraint string $P$ of length $r$, the…

We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…

The C/C++11 (C11) standard offers a spectrum of ordering guarantees on memory access operations. The combinations of such orderings pose a challenge in developing correct and efficient weak memory programs. A common solution to preclude…

We provide a differentially private algorithm for producing synthetic data simultaneously useful for multiple tasks: marginal queries and multitask machine learning (ML). A key innovation in our algorithm is the ability to directly handle…