Efficient learning of context-free grammars from positive structural examples

AbstractIn this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, Σ, P, S) is said to be reversible if (1) A → α and B → α in P implies A = B and (2) A → αBβ and A → αCβ in P implies B = C. We show that the class of reversible context-free grammars can be identified in the limit from positive samples of structural descriptions and there exists an efficient algorithm to identify them from positive samples of structural descriptions, where a structural description of a context-free grammar is an unlabelled derivation tree of the grammar. This implies that if positive structural examples of a reversible context-free grammar for the target language are available to the learning algorithm, the full class of context-free languages can be learned efficiently from positive samples

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Inklusion von Patternsprachen und verwandte Probleme

A pattern is a word that consists of variables and terminal symbols. The pattern language that is generated by a pattern A is the set of all terminal words that can be obtained from A by uniform replacement of variables with terminal words. For example, the pattern A = a x y a x (where x and y are variables, and the letter a is a terminal symbol) generates the set of all words that have some word a x both as prefix and suffix (where these two occurrences of a x do not overlap). Due to their simple definition, pattern languages have various connections to a wide range of other areas in theoretical computer science and mathematics. Among these areas are combinatorics on words, logic, and the theory of free semigroups. On the other hand, many of the canonical questions in formal language theory are surprisingly difficult. The present thesis discusses various aspects of the inclusion problem of pattern languages. It can be divide in two parts. The first one examines the decidability of pattern languages with a limited number of variables and fixed terminal alphabets. In addition to this, the minimizability of regular expressions with repetition operators is studied. The second part deals with descriptive patterns, the smallest generalizations of arbitrary languages through pattern languages ("smallest" with respect to the inclusion relation). Main questions are the existence and the discoverability of descriptive patterns for arbitrary languages.Ein Pattern ist ein Wort aus Variablen und Terminalsymbolen. Die von einem Pattern A erzeugte Patternsprache ist die Menge aller Terminalwörter, die durch eine uniforme Ersetzung der Variablen in A durch Terminalwörter erzeugt werden können. So beschreibt das Pattern A = a x y a x (wobei x und y Variablen sind und a ein Terminal ist) die Menge aller Wörter, die ein Wort der Form a x sowohl als Präfix, als auch als Suffix haben (ohne dass sich diese beiden Vorkommen von a x überlappen). Wegen ihrer einfachen Definition besitzen Patternsprachen eine Vielzahl von Verbindungen zu verschiedenen anderen Gebieten der theoretischen Informatik und Mathematik, unter anderem zur Wortkombinatorik, Logik und der Theorie freier Halbgruppen. Andererseits führen viele der üblichen sprachtheoretischen Fragestellungen bei Patternsprachen zu kombinatorischen Problemen von überraschender Schwierigkeit. Die vorliegende Dissertation widmet sich verschiedenen Aspekten des Inklusionsproblems von Patternsprachen und kann in zwei Teile unterteilt werden. Der erste Teil untersucht die Entscheidbarkeit des Inklusionsproblems für Sprachen, die von Pattern mit beschränkter Variablenzahl über Terminalalphabeten von beschränkter Größe erzeugt werden. Darüber hinaus werden verschiedene Aspekte der Minimierbarkeit von regulären Ausdrücken mit Rückreferenzen betrachtet. Der zweite Teil der Dissertation handelt von deskriptiven Pattern; d.h. denjenigen Pattern, die die (hinsichtlich der Inklusion) kleinsten Verallgemeinerungen einer gegebenen Sprache erzeugen. Hauptfragen sind hierbei die Existenz und die Auffindbarkeit deskriptiver Pattern für beliebige Sprachen

Head-Driven Phrase Structure Grammar

Head-Driven Phrase Structure Grammar (HPSG) is a constraint-based or declarative approach to linguistic knowledge, which analyses all descriptive levels (phonology, morphology, syntax, semantics, pragmatics) with feature value pairs, structure sharing, and relational constraints. In syntax it assumes that expressions have a single relatively simple constituent structure. This volume provides a state-of-the-art introduction to the framework. Various chapters discuss basic assumptions and formal foundations, describe the evolution of the framework, and go into the details of the main syntactic phenomena. Further chapters are devoted to non-syntactic levels of description. The book also considers related fields and research areas (gesture, sign languages, computational linguistics) and includes chapters comparing HPSG with other frameworks (Lexical Functional Grammar, Categorial Grammar, Construction Grammar, Dependency Grammar, and Minimalism)