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Showing papers on "Chomsky hierarchy published in 2011"


Journal ArticleDOI
TL;DR: In this article, the authors argue that there are (at least) eight main variations of the notion of the formal that are relevant for current discussions in philosophy and logic, and that they are structured in two main clusters, namely the formal as pertaining to forms, and the formalas pertaining to rules.
Abstract: What does it mean to say that logic is formal? The short answer is: it means (or can mean) several different things. In this paper, I argue that there are (at least) eight main variations of the notion of the formal that are relevant for current discussions in philosophy and logic, and that they are structured in two main clusters, namely the formal as pertaining to forms, and the formal as pertaining to rules. To the first cluster belong the formal as schematic; the formal as indifference to particulars; the formal as topic-neutrality; the formal as abstraction from intentional content; the formal as de-semantification. To the second cluster belong the formal as computable; the formal as pertaining to regulative rules; the formal as pertaining to constitutive rules. I analyze each of these eight variations, providing their historical background and raising related philosophical questions. The significance of this work of ‘conceptual archeology’ is that it may enhance clarity in debates where the notion o...

51 citations


Proceedings ArticleDOI
25 Sep 2011
TL;DR: Computer Science as a research discipline has always struggled with its identity and has inherited its research methods from the same disciplines: on the one hand, the mathematical approach with axioms, postulates and proofs; on the other hand the engineering approach with quantification, measurements and comparison.
Abstract: Computer Science as a research discipline has always struggled with its identity. On the one hand, it is a field deeply rooted in mathematics which resulted in strong theories.1 For example, there is computational complexity theory (turing machines, the halting problem), database theory (the relational model, expresive power of query languages), formal language theory (the chomsky hierarchy, well-formedness, formal semantics). On the other hand, it is a field deeply rooted in engineering which resulted in machines that have completely warped our society: the von Neumann architecture (the basis for digital computers), parallel processors (the new generation of multi-core machines), distributed computers (a prerequisite for the success of the internet and recent phenomena like grid computing). Consequently, computer science has inherited its research methods from the same disciplines: on the one hand, the mathematical approach with axioms, postulates and proofs; on the other hand the engineering approach with quantification, measurements and comparison.

21 citations


Posted Content
TL;DR: It is shown that it is decidable, given a circular splicing language and a regular language, whether they are equal, and it is proved the language generated by an alphabetic splicing system is context-free.
Abstract: In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature.

19 citations


Posted Content
TL;DR: An overview about relevant research to this topic during the last twenty years including own investigations and some new results is given and several generalizations of the notions of periodicity and primitivity of words are dedicated.
Abstract: In the algebraic theory of codes and formal languages, the set Q of all primitive words over some alphabet has received special inter- est. With this survey article we give an overview about relevant research to this topic during the last twenty years including own investigations and some new results. In Section 1 after recalling the most important notions from formal language theory we illustrate the connection between coding theory and primitive words by some facts. We dene primitive words as words having only a trivial representation as the power of another word. Nonprimitive words (without the empty word) are exactly the periodic words. Every nonempty word is a power of an uniquely determined prim- itive word which is called the root of the former one. The set of all roots of nonempty words of a language is called the root of the language. The primitive words have interesting combinatorial properties which we con- sider in Section 2. In Section 3 we investigate the relationship between the set Q of all primitive words over some xed alphabet and the lan- guage classes of the Chomsky Hierarchy and the contextual languages over the same alphabet. The computational complexity of the set Q and of the roots of languages are considered in Section 4. The set of all pow- ers of the same degree of all words from a language is the power of this language. We examine the powers of languages for dierent sets of ex- ponents, and especially their regularity and context-freeness, in Section 5, and the decidability of appropriate questions in Section 6. Section 7 is dedicated to several generalizations of the notions of periodicity and primitivity of words.

13 citations


01 Jan 2011
TL;DR: In this paper, the authors investigate generalized concatenation, which can be seen as a generalized version of chop operations, and prove non-closure properties under chop operations and incomparability to the family of languages that are the chop of two regular languages.
Abstract: We investigate chop operations, which can be seen as generalized concatenation. For several language families of the Chomsky hierarchy we prove (non)closure properties under chop operations and incomparability to the family of languages that are the chop of two regular languages. We also prove non-closure of that language family under Boolean operations and closure under reversal. Further, the representation of a regular language as the chop of two regular expressions can be exponentially more succinct than its regular expression. By considering the chop of two linear context-free languages we already obtain language families that have non-semi-decidable problems such as emptiness or finiteness.

13 citations


Journal ArticleDOI
TL;DR: The intent of this review is to list some bibliographic references regarding the recent progresses in the field of grammatical modeling of biological sequences and to briefly introduce basic knowledge about formal language theory, such as the Chomsky hierarchy, for non-experts in computational linguistics.
Abstract: Treating genomes just as languages raises the possibility of producing concise generalizations about information in biological sequences. Grammars used in this way would constitute a model of underlying biological processes or structures, and that grammars may, in fact, serve as an appropriate tool for theory formation. The increasing number of biological sequences that have been yielded further highlights a growing need for developing grammatical systems in bioinformatics. The intent of this review is therefore to list some bibliographic references regarding the recent progresses in the field of grammatical modeling of biological sequences. This review will also contain some sections to briefly introduce basic knowledge about formal language theory, such as the Chomsky hierarchy, for non-experts in computational linguistics, and to provide some helpful pointers to start a deeper investigation into this field.

10 citations


Proceedings ArticleDOI
20 Jun 2011
TL;DR: This paper defines a class of formal languages that capture the abstract behavior of robots which can be described as hybrid systems with stable continuous dynamics and shows that this class of languages falls within the Subregular hierarchy, thereby enabling computationally efficient operations between elements of the class.
Abstract: This paper brings together concepts from linguistics and formal language theory and applies them to model robot behavior. This is done by defining a class of formal languages that capture the abstract behavior of robots which can be described as hybrid systems with stable continuous dynamics. It is shown that this class of languages falls within the Subregular hierarchy, thereby enabling computationally efficient operations between elements of the class. Specifically, we show that the languages in question are Star-free, but do not belong into two well-known subclasses, members of which have been used in linguistics to construct models of natural language sound pattern acquisition.

10 citations


Journal ArticleDOI
Kaoru Fujioka1
TL;DR: New characterizations of regular, context-free, and recursively enumerable languages, using insertion systems with lower complexity are concerns by using both strictly locally testable languages and morphisms.
Abstract: This paper concerns new characterizations of regular, context-free, and recursively enumerable languages, using insertion systems with lower complexity. This is achieved by using both strictly locally testable languages and morphisms. The representation is in a similar way to the Chomsky-Schutzenberger representation of context-free languages. Specifically, each recursively enumerable language L can be represented in the form L=h(L(γ)∩R), where γ is an insertion system of weight (3,3), R is a strictly 2-testable language, and h is a projection. A similar representation can be obtained for context-free languages, using insertion systems of weight (2,0) and strictly 2-testable languages, as well as for regular languages, using insertion systems of weight (1,0) and strictly 2-testable languages.

9 citations


Book ChapterDOI
06 Jun 2011
TL;DR: A very abstract model of machine that simulates nature in a particular sense is introduced and a lower-bound on the number of memory states of such machines is proved if they were to simulate the experiment that corresponds to the Peres-Mermin square.
Abstract: In this paper we approach some questions about quantum contextuality with tools from formal logic In particular, we consider an experiment associated with the Peres-Mermin square The language of all possible sequences of outcomes of the experiment is classified in the Chomsky hierarchy and seen to be a regular language We introduce a very abstract model of machine that simulates nature in a particular sense A lower-bound on the number of memory states of such machines is proved if they were to simulate the experiment that corresponds to the Peres-Mermin square Moreover, the proof of this lower bound is seen to scale to a certain generalization of the Peres-Mermin square For this scaled experiment it is seen that the Holevo bound is violated and that the degree of violation increases uniformly

6 citations


01 Jan 2011
TL;DR: In this article, a grammar can be conceived as a theory that assigns the values of its notions to the sentences of a language, and propose the following basic relational notions for CHG: phrase structure, transformed structure, phonemic representation and phonetic representation.
Abstract: We defend that there is a link between the mathematical analytical models (characteristic of the structural tradition) and the mathematical synthetic models (characteristic of the generative tradition) that is peculiar to Chomsky’s grammar exposed in The Logical Structure of Linguistic Theory, CHG To identify this link helps to identify the objects and the task of the grammars in CHG and also to detect some inadequacies in the exposition and conception underlying in CHG (related to the connection between levels of representations, the conception of the objects and the conception of transformational representation) In order to clarify these inadequacies, we defend that a grammar can be conceived as a theory that assigns the values of its notions to the sentences of a language, and we propose the following basic relational notions for CHG: phrase structure, transformed structure, phonemic representation and phonetic representation By means of the structural metatheory, we define the potential models (after formulating the typifications and the characterizations of these notions) and the actual models of CHG (after formulating its fundamental law)

4 citations


Journal ArticleDOI
TL;DR: This paper mainly explores the language model presented by Comosky, Problem of Ambiguity, Degree of AmbIGuity, Approaches to Detect Ambigulence, comparisons of existing methods and recent trends etc.

Book ChapterDOI
06 Sep 2011
TL;DR: It is proved that probabilistic context-free grammars are more powerful than their non-probabilistic counterparts but in a way that is orthogonal to the Chomsky hierarchy.
Abstract: Over the last decade, probabilistic parsing has become the standard in the parsing literature where one of the purposes of those probabilities is to discard unlikely parses. We investigate the effect that discarding low probability parses has on both the weak and strong generative power of context-free grammars. We prove that probabilistic context-free grammars are more powerful than their non-probabilistic counterparts but in a way that is orthogonal to the Chomsky hierarchy. In particular, we show that the increase in power cannot be used to model any dependencies that discrete context-free grammars cannot.

Journal ArticleDOI
TL;DR: A new computing paradigm based on the idea of string folding is introduced, which is promising not only because of the expected theoretical results, but alsoBecause of the possible indirect applications in various fields (as for instance, mathematical linguistics, DNA computing, computing using light, and so on).
Abstract: The present paper introduces a new computing paradigm based on the idea of string folding. Comparisons between the computational power of the proposed model with the classical families of languages from the Chomsky hierarchy are studied. Some preliminary results are reported and some conjectures are discussed. In this respect, the proposed model is promising not only because of the expected theoretical results, but also because of the possible indirect applications in various fields (as for instance, mathematical linguistics, DNA computing, computing using light, and so on).

Proceedings ArticleDOI
03 Oct 2011
TL;DR: It was found that the evolutionary success rates of the classes of Regular and Context-Sensitive problems have no statistical difference in computational requirements, while the Context-Free class was found to be more difficult than the other two Chomsky problem classes through the statistical significance discovered when compared to the other classes.
Abstract: This paper presents an exploration into the relationship between Chomsky problem complexity, as defined by Theory of Computation, and the computational requirements to evolve solutions to these problems. Genetic programming is used to explore these computational requirements by evolving Turing machines that accept the languages posed. Quantifiable results are obtained by applying various metrics to the evolutionary success of these evolved Turing machines. The languages posed are samples out of three language classes from the Chomsky hierarchy, with each class having increasing levels of complexity based on the hierarchy. These languages are evolved on a two-tape Turing machine representation by making use of genetic operators found to be effective in the literature. By exploring the effects of the genetic programming algorithm population sizes and coupled genetic operator rates, it was found that the evolutionary success rates of the classes of Regular and Context-Sensitive problems have no statistical difference in computational requirements, while the Context-Free class was found to be more difficult than the other two Chomsky problem classes through the statistical significance discovered when compared to the other classes.

Posted Content
TL;DR: New computing models are proposed that feature (string) language acceptors with multiset manipulation as a computing mechanism, and it is shown that reaction automata are computationally Turing universal.
Abstract: Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy.

Journal ArticleDOI
TL;DR: It is shown that the power of such systems is large relative to the classic Chomsky Hierarchy, however, it is still able to algorithmically determine whether or not a string is a possible product of the iterated application of the operations.
Abstract: Transposable genetic elements are prevalent across many living organisms from bacteria to large mammals. Given the linear primary structure of genetic material, this process is natural to study from a theoretical perspective using formal language theory. We abstract the process of genetic transposition to operations on languages and study it combinatorially and computationally. It is shown that the power of such systems is large relative to the classic Chomsky Hierarchy. However, we are still able to algorithmically determine whether or not a string is a possible product of the iterated application of the operations.


Book ChapterDOI
Kaoru Fujioka1
19 Jul 2011
TL;DR: This work obtains some characterizations and representation theorems of context-free languages and regular languages in Chomsky hierarchy by insertion systems, strictly locally testable languages, and morphisms in the framework of Chomsky-Schutzenberger theorem.
Abstract: Representing a class of languages through operations on its subclasses is a traditional issue within formal language theory. Among the variety of representation theorems for context-free languages, Chomsky-Schutzenberger theorem is unique in that it consists of Dyck languages, regular languages, and simple operations. In this work, we obtain some characterizations and representation theorems of context-free languages and regular languages in Chomsky hierarchy by insertion systems, strictly locally testable languages, and morphisms in the framework of Chomsky-Schutzenberger theorem.

Proceedings ArticleDOI
10 Jul 2011
TL;DR: By defining the dependence of attributes, one type of partial order relation among sub-contexts is investigated in detail, and by introducing the notion of independence of a formal context, reduction of formal context is discussed.
Abstract: Formal concept analysis is one kind of efficient approaches for data analysis, formal context and concept lattice are two basic notions. In this paper, by defining the dependence of attributes, one type of partial order relation among sub-contexts is investigated in detail. In the meantime, by introducing the notion of independence of a formal context, reduction of formal context is discussed. Consequently, one type of partition of attribute set is obtained, and a hierarchical structure on the attributes set of formal context is revealed.