This document was created in addition to a recital for the seminar Pattern Matching at Chemnitz University of Technology in term 2001/2002. It is a description of basic text search approaches, which are the algorithms of Brute Force, Knuth-Morris-Pratt, Boyer-Moore and Boyer-Moore-Horspool. / Dieses Dokument entstand parallel zu einem Vortrag für das Proseminar Pattern Matching im Wintersemester 2001/2002 an der Technischen Universität Chemnitz. Es stellt die Funktionsweise der grundlegenden Suchalgorithmen Brute Force, Knuth-Morris-Pratt, Boyer-Moore sowie Boyer-Moore-Horspool dar.

In the last few decades, database management systems became powerful tools for storing large amount of data and executing complex queries over them. In addition to extended functionality, novel types of databases appear like triple stores, distributed databases, etc. Graph databases implementing the property-graph model belong to this development branch and provide a new way for storing and processing data in the form of a graph with nodes representing some entities and edges describing connections between them. This consideration makes them suitable for keeping data without a rigid schema for use cases like social-network processing or data integration. In addition to a flexible storage, graph databases provide new querying possibilities in the form of path queries, detection of connected components, pattern matching, etc. However, the schema flexibility and graph queries come with additional costs. With limited knowledge about data and little experience in constructing the complex queries, users can create such ones, which deliver unexpected results. Forced to debug queries manually and overwhelmed by the amount of query constraints, users can get frustrated by using graph databases. What is really needed, is to improve usability of graph databases by providing debugging and explaining functionality for such situations. We have to assist users in the discovery of what were the reasons of unexpected results and what can be done in order to fix them. The unexpectedness of result sets can be expressed in terms of their size or content. In the first case, users have to solve the empty-answer, too-many-, or too-few-answers problems. In the second case, users care about the result content and miss some expected answers or wonder about presence of some unexpected ones. Considering the typical problems of receiving no or too many results by querying graph databases, in this thesis we focus on investigating the problems of the first group, whose solutions are usually represented by why-empty, why-so-few, and why-so-many queries. Our objective is to extend graph databases with debugging functionality in the form of why-queries for unexpected query results on the example of pattern matching queries, which are one of general graph-query types. We present a comprehensive analysis of existing debugging tools in the state-of-the-art research and identify their common properties. From them, we formulate the following features of why-queries, which we discuss in this thesis, namely: holistic support of different cardinality-based problems, explanation of unexpected results and query reformulation, comprehensive analysis of explanations, and non-intrusive user integration. To support different cardinality-based problems, we develop methods for explaining no, too few, and too many results. To cover different kinds of explanations, we present two types: subgraph- and modification-based explanations. The first type identifies the reasons of unexpectedness in terms of query subgraphs and delivers differential graphs as answers. The second one reformulates queries in such a way that they produce better results. Considering graph queries to be complex structures with multiple constraints, we investigate different ways of generating explanations starting from the most general one that considers only a query topology through coarse-grained rewriting up to fine-grained modification that allows fine changes of predicates and topology. To provide a comprehensive analysis of explanations, we propose to compare them on three levels including a syntactic description, a content, and a size of a result set. In order to deliver user-aware explanations, we discuss two models for non-intrusive user integration in the generation process. With the techniques proposed in this thesis, we are able to provide fundamentals for debugging of pattern-matching queries, which deliver no, too few, or too many results, in graph databases implementing the property-graph model.

The thesis explains several algorithms for pattern matching. Algorithms work in both software and hardware. A part of the thesis is dedicated to extensions of finite automatons. The second part explains hashing and introduces concept of perfect hashing and CRC. The thesis also includes a suggestion of possible structure of a pattern matching unit based on deterministic finite automatons in FPGA. Experiments for determining the structure and size of resulting automatons were done in this thesis.

String matching algorithms are the algorithms used to search through different types of text in search of a certain pattern. Many of these algorithms achieve their impressive performance by analysing the pattern and saving that information. That information is then continuously used during the searching phase to know what parts of the text can be skipped. One such algorithm is the Berry-Ravindran. The Berry-Ravindran checks the two characters past the current try for a match and sees if those characters exist in the pattern. This thesis compares the Berry-Ravindran algorithm to new versions of itself that check three and four characters instead of two, along with the Boyer-Moore algorithm. Checking more characters improves the amount of the text that can be skipped by reducing the number of attempts needed but exponentially increases the pre-processing time. The improved performance in attempts does not necessarily mean a faster run-time because of the increased pre-processing time. The variable impacting the pre-processing time the biggest is the size of the alphabet that the text uses. This is researched by testing these algorithms with patterns ranging from 4 to 100 characters long on two different data sets. Protein data which has an alphabet size of 27 and DNA data which has an alphabet size of 4.

In March 2021, the EU launched the European Peace Facility (EPF), a financial instrument that allows the EU to commonly fund peacekeeping and military missions. However, following the Russian aggression against Ukraine on the 24th of February 2022, the EPF has primarily been used to provide Ukraine with lethal military equipment. This research uses a modified version of Flexible Pattern Matching to examine if the original intent and structure of the EPF are uniform with how it has been used by the EU to provide support for Ukraine. The result indicates that while there are some deviations from the intended and actual use of the EPF, the instrument has been vital in the EU’s rapid response to provide support to Ukraine. The research also highlights the normative power of the EPF, a key aspect of the instrument that was not predicted when it was launched. This analysis is relevant to both researchers and policymakers, offering insight into the EPF’s role in the EU’s hard power shift, while also providing suggestions for enhancing the EPF’s effectiveness in supporting Ukraine.

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Les structures avec des lieurs sont très communes en informatique. Les langages de programmation et les systèmes logiques sont des exemples de structures avec des lieurs. La manipulation de lieurs est délicate, de sorte que l’écriture de programmes qui ma- nipulent ces structures tirerait profit d’un soutien spécifique pour les lieurs. L’environ- nement de programmation Beluga est un exemple d’un tel système. Nous développons et présentons ici un compilateur pour ce système. Parmi les programmes pour lesquels Beluga est spécialement bien adapté, plusieurs peuvent bénéficier d’un compilateur. Par exemple, les programmes pour valider les types (les "type-checkers"), les compilateurs et les interpréteurs tirent profit du soutien spécifique des lieurs et des types dépendants présents dans le langage. Ils nécessitent tous également une exécution efficace, que l’on propose d’obtenir par le biais d’un compilateur. Le but de ce travail est de présenter un nouveau compilateur pour Beluga, qui emploie une représentation interne polyvalente et permet de partager du code entre plusieurs back-ends. Une contribution notable est la compilation du filtrage de Beluga, qui est particulièrement puissante dans ce langage. / In computer science, structures with variable binders are very common. Program- ming languages and logical frameworks are examples of structures with binders. Thus writing programs that deal with these kinds of data benefits with explicit support for data binding. The Beluga programming environment is an example of such a system. In this work we develop and present a compiler for the system. Many of the programs that Beluga is specially well suited for writing can benefit from a compiler. For example, some of the kinds programs that would benefit more are type-checkers, compilers and interpreters that take advantage of the binder support and dependent types present in the language, and also require a reasonably fast run-time. Our goal in this work, is to present a compiler for the Beluga system, that uses a very versatile internal representation that helps with the development of the system, and allows a sharing of code between several back-ends. Furthermore, we present a way of compiling the uniquely powerful pattern language supported by Beluga.

A árvore de sufixos é uma estrutura dados, que representa em espaço linear todos os fatores de uma palavra, com diversos exemplos de aplicações práticas. Neste trabalho, definimos uma estrutura mais geral: a árvore de Ukkonen. Provamos para ela diversas propriedades combinatórias, dentre quais, a minimalidade em um sentido preciso. Acreditamos que a apresentação aqui oferecida, além de mais geral que as árvores de sufixo, tem a vantagem de oferecer uma descrição explícita da topologia da árvore, de seus vértices, arestas e rótulos, o que não vimos em nenhum outro trabalho. Como aplicações, apresentamos também a árvore esparsa de sufixos (que armazena apenas um subconjunto dos sufixos) e a árvore de k-fatores (que armazena apenas os segmentos de comprimento k, ao invés dos sufixos) definidas como casos particulares das árvores de Ukkonen. Propomos para as árvores esparsas um novo algoritmo de construção com tempo O(n) e espaço O(m), onde n é tamanho da palavra e m é número de sufixos. Para as árvores de k-fatores, propomos um novo algoritmo online com tempo e espaço O(n), onde n é o tamanho da palavra. / The suffix tree is a data structure that represents, in linear space, all factors of a given word, with several examples of practical applications. In this work, we define a more general structure: the Ukkonen\'s tree. We prove many properties for it, among them, its minimality in a precise sense. We believe that this presentation, besides being more general than the suffix trees, has the advantage of offering an explicit description of the tree topology, its vertices, edges and labels, which was not seen in any other work. As applications, we also presents the sparse suffix tree (which stores only a subset of the suffixes) and the k-factor tree (which stores only the substrings of length k, instead of the suffixes), both defined as Ukkonen\'s tree special cases. We propose a new construction algorithm for the sparse suffix trees with time O(n) and space O(m), where n is the size of the word and m is the number of suffixes. For the k-factor trees, we propose a new online algorithm with time and space O(n), where n is the size of the word.

Title: Pattern matching in compilers Author: Ondřej Bílka Department: Department of Applied Mathematics Supervisor: Jan Hubička, Department of Applied Mathematics Abstract: In this thesis we develop tools for effective and flexible pattern matching. We introduce a new pattern matching system called amethyst. Amethyst is not only a generator of parsers of programming languages, but can also serve as an alternative to tools for matching regular expressions. Our framework also produces dynamic parsers. Its intended use is in the context of IDE (accurate syntax highlighting and error detection on the fly). Amethyst offers pattern matching of general data structures. This makes it a useful tool for implement- ing compiler optimizations such as constant folding, instruction scheduling, and dataflow analysis in general. The parsers produced are essentially top-down parsers. Linear time complexity is obtained by introducing the novel notion of structured grammars and reg- ularized regular expressions. Amethyst uses techniques known from compiler optimizations to produce effective parsers. Keywords: Packrat parsing, dynamic parsing, structured grammars, functional programming 1

La supervision automatique des processus industriels permet d'accroître la productivité et de diminuer le coût d'entretien. Le diagnostic est une composante principale d'un module de supervision. Il existe plusieurs approches pour réaliser le diagnostic. Les performances de chaque approche dépendent du problème posé. Nous cherchons une méthode de diagnostic capable de résoudre les problèmes suivants :<br />- dans une base de connaissance incomplète, tous les modes de fonctionnement ne sont pas représentés. En conséquence, un module de diagnostic doit être adaptatif afin d'inclure à sa base de connaissance les nouveaux modes dés qu'ils apparaissent,<br />- lorsque le système évolue vers un mode anormal ou non désiré, il est nécessaire d'anticiper cette évolution plutôt que d'attendre d'arriver à ce mode afin d'éviter ses conséquences surtout s'il est dangereux. Le module de diagnostic doit donc être prédictif,<br />- dans le cas d'un système évolutif, la base de connaissance doit être enrichie grâce à l'information apportée par les nouvelles observations. Cet enrichissement doit être réalisé en temps réel,<br />- les données sont à la fois incertaines et imprécises.<br />L'objectif principal de ma thèse consistait à mettre au point un module de diagnostic en temps réel adaptatif et prédictif pour des systèmes évolutifs, en utilisant les techniques de Reconnaissance des Formes, la théorie des ensembles flous et la théorie des possibilités. Ce module a été appliqué sur plusieurs applications industrielles.