Privileged Words and Sturmian Words

This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently. A word is privileged if it is a complete first return to a shorter privileged word, the shortest privileged words being letters and the empty word. Here we give and prove almost all results on privileged words known to date. On the other hand, the study of Sturmian words is a well-established topic in combinatorics on words. In this dissertation, we focus on questions concerning repetitions in Sturmian words, reproving old results and giving new ones, and on establishing completely new research directions. The study of privileged words presented in this dissertation aims to derive their basic properties and to answer basic questions regarding them. We explore a connection between privileged words and palindromes and seek out answers to questions on context-freeness, computability, and enumeration. It turns out that the language of privileged words is not context-free, but privileged words are recognizable by a linear-time algorithm. A lower bound on the number of binary privileged words of given length is proven. The main interest, however, lies in the privileged complexity functions of the Thue-Morse word and Sturmian words. We derive recurrences for computing the privileged complexity function of the Thue-Morse word, and we prove that Sturmian words are characterized by their privileged complexity function. As a slightly separate topic, we give an overview of a certain method of automated theorem-proving and show how it can be applied to study privileged factors of automatic words. The second part of this dissertation is devoted to Sturmian words. We extensively exploit the interpretation of Sturmian words as irrational rotation words. The essential tools are continued fractions and elementary, but powerful, results of Diophantine approximation theory. With these tools at our disposal, we reprove old results on powers occurring in Sturmian words with emphasis on the fractional index of a Sturmian word. Further, we consider abelian powers and abelian repetitions and characterize the maximum exponents of abelian powers with given period occurring in a Sturmian word in terms of the continued fraction expansion of its slope. We define the notion of abelian critical exponent for Sturmian words and explore its connection to the Lagrange spectrum of irrational numbers. The results obtained are often specialized for the Fibonacci word; for instance, we show that the minimum abelian period of a factor of the Fibonacci word is a Fibonacci number. In addition, we propose a completely new research topic: the square root map. We prove that the square root map preserves the language of any Sturmian word. Moreover, we construct a family of non-Sturmian optimal squareful words whose language the square root map also preserves.This construction yields examples of aperiodic infinite words whose square roots are periodic.

RTOS Framework for Real-Time Control System

This thesis is done as a complementary part for the active magnet bearing (AMB) control software development project in Lappeenranta University of Technology. The main focus of the thesis is to examine an idea of a real-time operating system (RTOS) framework that operates in a dedicated digital signal processor (DSP) environment. General use real-time operating systems do not necessarily provide sufficient platform for periodic control algorithm utilisation. In addition, application program interfaces found in real-time operating systems are commonly non-existent or provided as chip-support libraries, thus hindering platform independent software development. Hence, two divergent real-time operating systems and additional periodic extension software with the framework design are examined to find solutions for the research problems. The research is discharged by; tracing the selected real-time operating system, formulating requirements for the system, and designing the real-time operating system framework (OSFW). The OSFW is formed by programming the framework and conjoining the outcome with the RTOS and the periodic extension. The system is tested and functionality of the software is evaluated in theoretical context of the Rate Monotonic Scheduling (RMS) theory. The performance of the OSFW and substance of the approach are discussed in contrast to the research theme. The findings of the thesis demonstrates that the forged real-time operating system framework is a viable groundwork solution for periodic control applications.

Comparison between dSPACE and NI systems based on real-time intelligent control of a teleoperated hydraulic servo system

The Laboratory of Intelligent Machine researches and develops energy-efficient power transmissions and automation for mobile construction machines and industrial processes. The laboratory's particular areas of expertise include mechatronic machine design using virtual technologies and simulators and demanding industrial robotics. The laboratory has collaborated extensively with industrial actors and it has participated in significant international research projects, particularly in the field of robotics. For years, dSPACE tools were the lonely hardware which was used in the lab to develop different control algorithms in real-time. dSPACE's hardware systems are in widespread use in the automotive industry and are also employed in drives, aerospace, and industrial automation. But new competitors are developing new sophisticated systems and their features convinced the laboratory to test new products. One of these competitors is National Instrument (NI). In order to get to know the specifications and capabilities of NI tools, an agreement was made to test a NI evolutionary system. This system is used to control a 1-D hydraulic slider. The objective of this research project is to develop a control scheme for the teleoperation of a hydraulically driven manipulator, and to implement a control algorithm between human and machine interaction, and machine and task environment interaction both on NI and dSPACE systems simultaneously and to compare the results.

Defining Contexts in Context-Free Grammars

This thesis introduces an extension of Chomsky’s context-free grammars equipped with operators for referring to left and right contexts of strings.The new model is called grammar with contexts. The semantics of these grammars are given in two equivalent ways — by language equations and by logical deduction, where a grammar is understood as a logic for the recursive definition of syntax. The motivation for grammars with contexts comes from an extensive example that completely defines the syntax and static semantics of a simple typed programming language. Grammars with contexts maintain most important practical properties of context-free grammars, including a variant of the Chomsky normal form. For grammars with one-sided contexts (that is, either left or right), there is a cubic-time tabular parsing algorithm, applicable to an arbitrary grammar. The time complexity of this algorithm can be improved to quadratic,provided that the grammar is unambiguous, that is, it only allows one parsefor every string it defines. A tabular parsing algorithm for grammars withtwo-sided contexts has fourth power time complexity. For these grammarsthere is a recognition algorithm that uses a linear amount of space. For certain subclasses of grammars with contexts there are low-degree polynomial parsing algorithms. One of them is an extension of the classical recursive descent for context-free grammars; the version for grammars with contexts still works in linear time like its prototype. Another algorithm, with time complexity varying from linear to cubic depending on the particular grammar, adapts deterministic LR parsing to the new model. If all context operators in a grammar define regular languages, then such a grammar can be transformed to an equivalent grammar without context operators at all. This allows one to represent the syntax of languages in a more succinct way by utilizing context specifications. Linear grammars with contexts turned out to be non-trivial already over a one-letter alphabet. This fact leads to some undecidability results for this family of grammars

Real-time monitoring of laser scribing process utilizing high-speed camera

Currently, laser scribing is growing material processing method in the industry. Benefits of laser scribing technology are studied for example for improving an efficiency of solar cells. Due high-quality requirement of the fast scribing process, it is important to monitor the process in real time for detecting possible defects during the process. However, there is a lack of studies of laser scribing real time monitoring. Commonly used monitoring methods developed for other laser processes such a laser welding, are sufficient slow and existed applications cannot be implemented in fast laser scribing monitoring. The aim of this thesis is to find a method for laser scribing monitoring with a high-speed camera and evaluate reliability and performance of the developed monitoring system with experiments. The laser used in experiments is an IPG ytterbium pulsed fiber laser with 20 W maximum average power and Scan head optics used in the laser is Scanlab’s Hurryscan 14 II with an f100 tele-centric lens. The camera was connected to laser scanner using camera adapter to follow the laser process. A powerful fully programmable industrial computer was chosen for executing image processing and analysis. Algorithms for defect analysis, which are based on particle analysis, were developed using LabVIEW system design software. The performance of the algorithms was analyzed by analyzing a non-moving image from the scribing line with resolution 960x20 pixel. As a result, the maximum analysis speed was 560 frames per second. Reliability of the algorithm was evaluated by imaging scribing path with a variable number of defects 2000 mm/s when the laser was turned off and image analysis speed was 430 frames per second. The experiment was successful and as a result, the algorithms detected all defects from the scribing path. The final monitoring experiment was performed during a laser process. However, it was challenging to get active laser illumination work with the laser scanner due physical dimensions of the laser lens and the scanner. For reliable error detection, the illumination system is needed to be replaced.