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String Covering: A Survey

Mhaskar Neerja, Smyth W.F.

Fundamenta Informaticae

2022

Vol. 190, nr 1

17--45

The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one potential compaction methodology, the cover of a given string x, initially proposed in a simple form in 1990, but increasingly of interest as more sophisticated variants have been discovered. We then consider covering by a seed; that is, a cover of a superstring of x. We conclude with many proposals for research directions that could make significant contributions to string processing in future.

Regular and chaotic dynamics of a 4-DOF mechanical system with dry friction

Kosińska A., Awrejcewicz J., Grzelczyk D.

Vibrations in Physical Systems

2016

Vol. 27

195--202

In this paper the model of four degree-of-freedom mechanical sliding system with dry friction is considered. One of the components of the mentioned system rides on driving belt, which is driven at constant velocity. This model corresponds to a row of carriage laying on a guideway, which moves at constant velocity with respect to the guideway as a foundation. From a mathematical point of view the analyzed problem is governed by four second order differential equations of motion, and numerical analysis is performed in Mathematica software. Some interesting behaviors are detected and reported using Phase Portraits, Poincaré Maps and Lyapunov Exponents. Moreover, Power Spectral Densities obtained by the Fast Fourier Transform technique are reported. The presented results show different behaviors of the system, including periodic, quasi-periodic and chaotic orbits.

ω-rewriting the Collatz problem

Scollo G.

Fundamenta Informaticae

2005

Vol. 64, nr 1-4

405-416

The Collatz problem is comprised of two distinct, separate questions: existence of eventually periodic Collatz reductions with a nontrivial period, and existence of period-free Collatz reductions. This paper introduces a few distinct, related formalizations of the Collatz dynamics as term rewriting systems, using elementary concepts from the theory of state transition dynamics. Some of the subject systems act on finite terms, whereas others rewrite terms that are endowed with a countable, recursively defined structure. The latter presents a convenient framework for the investigation of extensions of the Collatz dynamics to dense systems.