Related papers: Properties of maximum Lempel-Ziv complexity string…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
We consider the Shannon cipher system in the framework of individual sequences and finite-state encrypters under the metric of maximal leakage of information. A lower bound and an asymptotically matching upper bound on the leakage are…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
A new set of boundary conditions for string propagators is proposed in this paper. The boundary conditions are parametrized by a complex number $\lambda$. Under these new boundary conditions, the left-moving and right-moving modes are…
We study the dynamical stability of the BTZ black string against fermonic and gravitational perturbations. The BTZ black string is not always stable against these perturbations. There exist threshold values for $m^2$ related to the…
Lempel-Ziv (LZ77) factorization is a fundamental problem in string processing: Greedily partition a given string $T$ from left to right into blocks (called phrases) so that each phrase is either the leftmost occurrence of a letter or the…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly.…
Lempel-Ziv-Double (LZD) is a variation of the LZ78 compression scheme that achieves better compression on repetitive datasets. Nevertheless, prior research has identified computational inefficiencies and a weakness in its compressibility…
We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, $r$, of runs in the run-length encoding of the Burrows--Wheeler transform (BWT) can…
Special kind of closed strings is considered. It is shown that these closed strings behave as two (an even number of) open strings at the classical level and one open string at the quantum level. They contain massless vector field in their…
For the relativistic string with massive ends arbitrary small disturbances of the uniform rotation of the rectilinear string are investigated. There are two classes of these oscillations with different spectra of frequencies. They are…
The string equivalent of a massless particle ($m=0$) is the tensionless string ($T=0$). The study of such strings is of interest when trying to understand the high energy limit of ordinary strings. I discuss the classical $T\to 0$ limit of…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of…
In this paper we present $LCSk$++: a new metric for measuring the similarity of long strings, and provide an algorithm for its efficient computation. With ever increasing size of strings occuring in practice, e.g. large genomes of plants…
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…
Longest Run Subsequence is a problem introduced recently in the context of the scaffolding phase of genome assembly (Schrinner et al., WABI 2020). The problem asks for a maximum length subsequence of a given string that contains at most one…
The interplay of shaped signaling and fiber nonlinearities is reviewed in the asymptotic and finite-length regime. We present explanations and discuss implications of an optimum shaping length of just a few hundred symbols.
Lempel-Ziv complexity (LZC) is a key measure for detecting the irregularity and complexity of nonlinear time series and has seen various improvements in recent decades. However, existing LZC-based metrics, such as Permutation Lempel-Ziv…