Related papers: Properties of maximum Lempel-Ziv complexity string…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
The Lempel-Ziv 77 (LZ77) factorization is a fundamental compression scheme widely used in text processing and data compression. In this work, we investigate the time complexity of maintaining the LZ77 factorization of a dynamic string. By…
Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…
We initiate a study of a new model of property testing that is a hybrid of testing properties of distributions and testing properties of strings. Specifically, the new model refers to testing properties of distributions, but these are…
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…
Results of an exhaustive search for minimum peak sidelobe level binary sequences are presented. Several techniques for efficiency implementation of search algorithm are described. A table of number of non-equivalent optimal binary sequences…
The combined Universal Probability M(D) of strings x in sets D is close to max M({x}) over x in D: their ~logs differ by at most D's information j=I(D:H) about the halting sequence H. Thus if all x have complexity K(x) >k, D carries >i bits…
Long-lived particles (LLPs) provide an unambiguous signal for physics beyond the Standard Model (BSM). They have a distinct detector signature, with decay lengths corresponding to lifetimes of around nanoseconds or longer. Lepton colliders…
We consider extensions of the standard model containing additional heavy particles ("quirks") charged under a new unbroken non-abelian gauge group as well as the standard model. We assume that the quirk mass m is in the phenomenologically…
Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS)…
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…
This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated…
We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common…
We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that…
We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when…
The deep imaging of the field of an observed lensing event by a cosmic string reveals many additional lensing events. We study the statistics of such string lensing. We derive explicit expressions for the distributions of image separations…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…
This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…
The LZ-End parsing [Kreft & Navarro, 2011] of an input string yields compression competitive with the popular Lempel-Ziv 77 scheme, but also allows for efficient random access. Kempa and Kosolobov showed that the parsing can be computed in…
In a previous paper, we proposed a probability interpretation for higher genus amplitudes of BMN (Berenstein-Maldacena-Nastase) strings in a pp-wave background with infinite negative curvature. This provides a natural definition of the…