Chomsky hierarchy

About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.

The theory of grammar constraints

Abstract: By introducing the Regular Membership Constraint, Gilles Pesant pioneered the idea of basing constraints on formal languages. The paper presented here is highly motivated by this work, taking the obvious next step, namely to investigate constraints based on grammars higher up in the Chomsky hierarchy. We devise an arc-consistency algorithm for context-free grammars, investigate when logic combinations of grammar constraints are tractable, show how to exploit non-constant size grammars and reorderings of languages, and study where the boundaries run between regular, context-free, and context-sensitive grammar filtering.

Desperately evolving syntax

Abstract: The Chomsky Hierarchy (CH) gives a first approximation as to where human syntax lies in an abstract logical space: the generating device accepting appropriate languages should be slightly more powerful than a standard Push-Down Automaton (a PDA+), although for familiar reasons not much more so. An evolutionary study of syntax ought to give us some clues as to how a PDA+ could have emerged in brains. The goal of my talk is to provide an approach to this question that is informed about contemporary considerations in the Eva-Devo paradigm and, especially, standard results in the study of syntax

Theory of Computing: A Gentle Introduction

Abstract: THEORY OF COMPUTING: A GENTLE INTRODUCTION by Efim Kinber and Carl Smith Prentice-Hall, Inc., 2001, 207 pp. Theory of Computing: A Gentle Introduction is a textbook on the theory of computing written for a one-semester course emphasizing the fundamental notions and results in languages, automata, and computation. The book is written in a nice conversational style that students will find inviting. I used this text in my one-semester theory of computation course and was easily able to work through the entire text. Students who have completed a semester of discrete mathematics including propositional logic and graph theory will be able to handle the text and exercises of this thin and unimposing text. There are fewer exercises than we are used to in mathematics texts, but the exercises are well-chosen and an instructor can assign all of them without overloading the student. A drawback for the student, but a plus for the instructor wanting class discussion is the absence of solutions to the exercises. I have not seen another book like Theory of Computing: A Gentle Introduction on the market. The authors want to deliver the topics from the point of view of relevance to computer science and are willing to sacrifice some topics and rigor to make that delivery. The text may best be described as a light version of Lewis and Papadimitriou's well-known Elements in the Theory of Computation (Prentice-Hall). Indeed, the Kinber and Smith text parallel's Lewis and Papadimitriou in content, organization (including chapter numbers and titles), and notation. Theory of Computing: A Gentle Introduction begins with an introductory chapter that reviews set theory, equivalence relations, functions, and the pigeonhole principle. Students fresh out of their course in discrete mathematics will have little need for this chapter. Chapter 2 is concerned with finite automata. The authors provide clear exposition and relevant examples for their discussion of deterministic and nondeterministic finite automata and regular expressions. The text includes discussion and proofs of some major theorems, including the equivalence of deterministic and nondeterministic automata, Kleene's theorem that the language accepted by a finite automaton is regular, the pumping lemma for regular languages, and indirectly and constructively, the Myhill-Nerode theorem. Chapter 3 of Theory of Computing: A Gentle Introduction is devoted to context-free languages. Following very closely the presentation of Lewis and Papadimitriou, Kinber and Smith take the reader through the basic notions of context-free grammars, parse trees (emphasizing the notion of ambiguous grammars), pushdown automata, closure properties, the pumping lemma for context-free languages, Chomsky normal form, and determinism. No membership algorithms for context-free grammars are presented in the book, so I added the CYK algorithm as a supplementary topic. Inexplicably (from the point of view of a language theorist), Theory of Computing: A Gentle Introduction offers no discussion of the Chomsky hierarchy of languages. …