相关论文: A Separation Between Run-Length SLPs and LZ77

The Erd\H{o}s-Ginzburg-Ziv theorem states that for any sequence of $2n-1$ integers, there exists a subsequence of $n$ elements whose sum is divisible by $n$. In this article, we provide a simple, practical $O(n\log\log n)$ algorithm and a…

A border of a string is a non-empty prefix of the string that is also a suffix of the string, and a string is unbordered if it has no border other than itself. Loptev, Kucherov, and Starikovskaya [CPM 2015] conjectured the following: If we…

Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…

In this paper, we study lower bounds of a general family of $L$-functions on the $1$-line. More precisely, we show that for any $F(s)$ in this family, there exists arbitrary large $t$ such that $F(1+it)\geq e^{\gamma_F} (\log_2 t + \log_3…

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…

Fix a prime $p$ and an integer $m$ with $p> m \geq 2$. Define the family of finite groups \[ G_n :=SL_m (\mathbb{Z}/p^{n}\mathbb{Z}) \] for $n=1,2,... $. We will prove that there exist two positive constants $C$ and $d$ such that for any…

A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…

The repetition threshold is the smallest real number $\alpha$ such that there exists an infinite word over a $k$-letter alphabet that avoids repetition of exponent strictly greater than $\alpha$. This notion can be generalized to graph…

Previous work by Demaine et al. (2012) developed a strong connection between smallest context-free grammars and staged self-assembly systems for one-dimensional strings and assemblies. We extend this work to two-dimensional polyominoes and…

Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…

We study circuit codes with long bit runs (sequences of distinct transitions) and derive a formula for the maximum length for an infinite class of symmetric circuit codes with long bit runs. This formula also results in an improved lower…

Every finite group $G$ has a normal series each of whose factors is either a solvable group or a direct product of non-abelian simple groups. The minimum number of nonsolvable factors, attained on all possible such series in $G$, is called…

In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…

It is commonly believed that the normalized gaps between consecutive ordinates $t_n$ of the zeros of the Riemann zeta function on the critical line can be arbitrarily large. In particular, drawing on analogies with random matrix theory, it…

We show that the number of $t$-ary trees with path length equal to $p$ is $\exp(h(t^{-1})t\log t \frac{p}{\log p}(1+o(1)))$, where $\entropy(x){=}{-}x\log x {-}(1{-}x)\log (1{-}x)$ is the binary entropy function. Besides its intrinsic…

The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix $p$ is denoted $L(p)$. When $p$ is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence.…

This paper deals with the Mittag-Leffler polynomials (MLP) by extracting their essence which consists of real polynomials with fine properties. They are orthogonal on the real line instead of the imaginary axes for MLP. Beside recurrence…

We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of what was known as the "runs" conjecture (Kolpakov \& Kucherov (FOCS '99)), which states that the…

Log data provides crucial insights for tasks like monitoring, root cause analysis, and anomaly detection. Due to the vast volume of logs, automated log parsing is essential to transform semi-structured log messages into structured…

We show that, given a string $s$ of length $n$, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates $s$ and only $s$ and whose size is within an $\Oh{\min (g \log…