Showing papers on "Chomsky hierarchy published in 2002"
TL;DR: It is shown that context-free valence grammars over finite monoids or commutative monoids have the same power as valence Grammar over finite groups or Commutative groups, respectively.
50 citations
TL;DR: The study of those P systems where the computation is performed by the communication of objects, that is, systems with symport and antiport rules is continued, and a characterization of recursively enumerable languages is obtained.
Abstract: We continue here the study of those P systems where the computation is performed by the communication of objects, that is, systems with symport and antiport rules. Instead of the (number of) objects collected in a specified membrane, as the result of a computation we consider the itineraries of a certain object through membranes, during a halting computation, written as a coding of the string of labels of the visited membranes. The family of languages generated in this way is investigated with respect to its place in the Chomsky hierarchy. When the (symport and antiport) rules are applied in a conditional manner, promoted or inhibited by certain objects which should be present in the membrane where a rule is applied, then a characterization of recursively enumerable languages is obtained; the power of systems with the rules applied freely is only partially described.
14 citations
TL;DR: This work considers simulating finite automata (both deterministic and nondeterministic) with context-free grammars in Chomsky normal form (CNF), and shows that any unary DFA with n states can be simulated by a CNF grammar with O(n1/3) variables.
13 citations
Journal Article•
TL;DR: In this paper, a strict four-level hierarchy of graphs closely related to the Chomsky hierarchy of formal languages is considered and a uniform presentation of the four families by means of string rewriting is provided.
Abstract: We consider a strict four-level hierarchy of graphs closely related to the Chomsky hierarchy of formal languages. We provide a uniform presentation of the four families by means of string rewriting.
12 citations
26 Aug 2002
TL;DR: A strict four-level hierarchy of graphs closely related to the Chomsky hierarchy of formal languages is considered, and a uniform presentation of the four families is provided by means of string rewriting.
Abstract: We consider a strict four-level hierarchy of graphs closely related to the Chomsky hierarchy of formal languages We provide a uniform presentation of the four families by means of string rewriting
12 citations
Journal Article•
TL;DR: 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) in content, organization, and notation.
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. …
4 citations
Journal Article•
TL;DR: By introducing a new operation, the exponentiation of formal languages, it turns out that some well known families of languages are closed under this exponentiation, e.
Abstract: By introducing a new operation, the exponentiation of formal languages, we can define Heyting algebras of formal languages. It turns out that some well known families of languages are closed under this exponentiation, e. g., the families of regular and of context-sensitive languages.
2 citations
TL;DR: It is shown that the classes of languages obtained in this way are recognizable in polynomial time provided that all components of the pattern interpretation are injective homomorphisms.
Abstract: A word w is obtained by an ordered n-pattern interpretation of a word x if there are n homomorphisms h
1,h2,ċċċ, hn such that w=h1(x)h2(x)ċs hn(x). This ordered multiple pattern interpretation is naturally extended to languages. We show a strong relationship between the family of languages obtained by ordered multiple pattern interpretations of regular, linear, and context-free languages and the family of regular, linear, and context-free simple matrix languages. Concepts of ambiguity and inherent ambiguity of ordered multiple pattern interpretation are defined and it is shown that these properties are not decidable on the class of context-free languages. Then, we investigate arbitrary multiple pattern interpretations of the same classes of languages in the Chomsky hierarchy. We show that the classes of languages obtained in this way are recognizable in polynomial time provided that all components of the pattern interpretation are injective homomorphisms. We also present a series of open problems.
2 citations
01 Jan 2002
TL;DR: A fifth language accepting machine called the PDA-T is introduced, some of its interesting formalproperties are demonstrated, and its role in the §-Calculus 1 is shown, and a formal language classifica-tion (the §-Hierarchy) is proposed, derived largely from the Chomsky Hierarchy, but with a fifth class of language accepted by the Pda-T.
Abstract: We introduce a fifth language accepting machine calledthe PDA-T, demonstrate some of its interesting formalproperties, and show its role in the §-Calculus 1 . Basedupon this new machine and the §-Calculus’ other prop-erties, we demonstrate the §-Calculus’ formal TuringPower, and then propose a formal language classifica-tion (the §-Hierarchy), derived largely from the ChomskyHierarchy, but with a fifth class of language accepted bythe PDA-T. We show that this modified hierarchy yieldsseveral conceptual benefits over the standard four ma-chine Chomsky Hierarchy. We also provide some practi-cal examples of the use of §-grammars in context-sensitive and semantic parsing. Keywords: context-sensitive parsing, adaptive gram-mars, §-Calculus, push down automata, predicatedparsing, Chomsky Hierarchy 1 Introduction The efficient parsing of context-sensitive lan-guages holds the interest of many researchers, sinceit has application in natural language parsing[Boullier 1998], in the formalization of program-ming language semantics [Christiansen 1988 andmany others], and in the solution of classically dif-ficult to parse languages [Boullier 1999b]. Al-though linguistic formalisms such as those first in-troduced by [Chomsky] technically and theoreti-cally allow for the parsing of all decidable lan-guages, pure grammar formalisms can be somewhatcumbersome to work with when attempting to writecorrect grammars for non-trivial Type < 2 lan-guages, and moreover, devising efficient algorithmsto process the formalisms is a difficult problem.Many different syntactic extensions to standardpure grammar formalisms have been suggested:from [van Wijngaarden] grammars, to attribute
1 citations
Journal Article•
TL;DR: A possible infinite natural number is associated with each production/nonterminal of a grammar which restricts its possibility to participate arbitrarily many times in the string generation, and it is proved that this restriction does not lead to an increase in the computational power.
Abstract: In the present paper we discuss a limitation of the resources activation (productions or nonterminals) of a Chomsky grammar. We associate a possible infinite natural number with each production/nonterminal of a grammar which restricts its possibility to participate arbitrarily many times in the string generation. This number may be viewed as the lifetime of that resource. We prove that this restriction does not lead to an increase in the computational power. A specific descriptional complexity criterion, namely the minimal number of immortal productions/nonterminals of a grammar and its extension to languages is investigated. Finally, we define grammars with bounded-frequency resources and prove that they are more powerful than grammars with bounded-life resources.
1 citations
Book•
27 Mar 2002
TL;DR: The Root of a Language and Its Complexity, the Power of One-Letter Rational Languages, and some Regular Languages That Are Church-Rosser Congruential are among the topics discussed.
Abstract: Invited Presentations.- Automata: From Uncertainty to Quantum.- Elementary Theory of Ordinals with Addition and Left Translation by ?.- The Equational Theory of Fixed Points with Applications to Generalized Language Theory.- Second-Order Logic over Strings: Regular and Non-regular Fragments.- Decision Questions on Integer Matrices.- Some Petri Net Languages and Codes.- Words, Permutations, and Representations of Numbers.- Proof Complexity of Pigeonhole Principles.- Words and Patterns.- A Short Introduction to Infinite Automata.- Contributions.- The Power of One-Letter Rational Languages.- The Entropy of Lukasiewicz-Languages.- Collapsing Words vs. Synchronizing Words.- A Note on Synchronized Automata and Road Coloring Problem.- Shuffle Quotient and Decompositions.- The Growing Context-Sensitive Languages Are the Acyclic Context-Sensitive Languages.- Recognizable Sets of N-Free Pomsets Are Monadically Axiomatizable.- Automata on Series-Parallel Biposets.- Hierarchies of String Languages Generated by Deterministic Tree Transducers.- Partially-Ordered Two-Way Automata: A New Characterization of DA.- Level 5/2 of the Straubing-Therien Hierarchy for Two-Letter Alphabets.- On the Power of Randomized Pushdown Automata.- The Root of a Language and Its Complexity.- Valuated and Valence Grammars: An Algebraic View.- Context-Free Valence Grammars - Revisited.- An Undecidability Result Concerning Periodic Morphisms.- A Universal Turing Machine with 3 States and 9 Symbols.- Minimal Covers of Formal Languages.- Some Regular Languages That Are Church-Rosser Congruential.- On the Relationship between the McNaughton Families of Languages and the Chomsky Hierarchy.- Forbidden Factors and Fragment Assembly.- Parallel Communicating Grammar Systems with Incomplete Information Communication.- Eliminating Communication by Parallel Rewriting.- String Rewriting Sequential P-Systems and Regulated Rewriting.