Showing papers on "Chomsky hierarchy published in 2015"

Principles of structure building in music, language and animal song

Abstract: Human language, music and a variety of animal vocalizations constitute ways of sonic communication that exhibit remarkable structural complexity. While the complexities of language and possible parallels in animal communication have been discussed intensively, reflections on the complexity of music and animal song, and their comparisons, are underrepresented. In some ways, music and animal songs are more comparable to each other than to language as propositional semantics cannot be used as indicator of communicative success or wellformedness, and notions of grammaticality are less easily defined. This review brings together accounts of the principles of structure building in music and animal song. It relates them to corresponding models in formal language theory, the extended Chomsky hierarchy (CH), and their probabilistic counterparts. We further discuss common misunderstandings and shortcomings concerning the CH and suggest ways to move beyond. We discuss language, music and animal song in the context of their function and motivation and further integrate problems and issues that are less commonly addressed in the context of language, including continuous event spaces, features of sound and timbre, representation of temporality and interactions of multiple parallel feature streams. We discuss these aspects in the light of recent theoretical, cognitive, neuroscientific and modelling research in the domains of music, language and animal song.

Grammatical Inference for Computational Lingustics

Abstract: This book provides a thorough introduction to the subfield of theoretical computer science known as grammatical inference from a computational linguistic perspective. Grammatical inference provides principled methods for developing computationally sound algorithms that learn structure from strings of symbols. The relationship to computational linguistics is natural because many research problems in computational linguistics are learning problems on words, phrases, and sentences: What algorithm can take as input some finite amount of data (for instance a corpus, annotated or otherwise) and output a system that behaves "correctly" on specific tasks? Throughout the text, the key concepts of grammatical inference are interleaved with illustrative examples drawn from problems in computational linguistics. Special attention is paid to the notion of "learning bias." In the context of computational linguistics, such bias can be thought to reflect common (ideally universal) properties of natural languages. This bias can be incorporated either by identifying a learnable class of languages which contains the language to be learned or by using particular strategies for optimizing parameter values. Examples are drawn largely from two linguistic domains (phonology and syntax) which span major regions of the Chomsky Hierarchy (from regular to context-sensitive classes). The conclusion summarizes the major lessons and open questions that grammatical inference brings to computational linguistics.

A Formal Language Model of DNA Polymerase Enzymatic Activity

Abstract: We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v called primer is Watson-Crick complementary and can thus bind to a substring of the longer string u called template the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. We call this language operation L1-directed extension of L2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution the minimal primer language to this question.

Does Formal Complexity Reflect Cognitive Complexity? Investigating Aspects of the Chomsky Hierarchy in an Artificial Language Learning Study

Abstract: This study investigated whether formal complexity, as described by the Chomsky Hierarchy, corresponds to cognitive complexity during language learning. According to the Chomsky Hierarchy, nested dependencies (context-free) are less complex than cross-serial dependencies (mildly context-sensitive). In two artificial grammar learning (AGL) experiments participants were presented with a language containing either nested or cross-serial dependencies. A learning effect for both types of dependencies could be observed, but no difference between dependency types emerged. These behavioral findings do not seem to reflect complexity differences as described in the Chomsky Hierarchy. This study extends previous findings in demonstrating learning effects for nested and cross-serial dependencies with more natural stimulus materials in a classical AGL paradigm after only one hour of exposure. The current findings can be taken as a starting point for further exploring the degree to which the Chomsky Hierarchy reflects cognitive processes.

Compressibility of Finite Languages by Grammars

Abstract: We consider the problem of simultaneously compressing a finite set of words by a single grammar. The central result of this paper is the construction of an incompressible sequence of finite word languages. This result is then shown to transfer to tree languages and (via a previously established connection between proof theory and formal language theory) also to formal proofs in first-order predicate logic.

Teaching-learning methodology for formal languages and automata theory

Abstract: Formal languages and automata (FLA) theory have fundamental relevance to the base of knowledge in the computer science area, especially focusing on scientific education. Usually presented by a discipline, the teaching-learning process of FLA is characterized by the high level of abstraction, and it is considered difficult due to the complexity of language formalisms. As support for the learning process, tools have been used to simulate language formalisms. However, the simulation is not enough to reinforce the construction of an abstract concept. In this paper, we present an FLA teaching-learning methodology based on the development of simulators as an approach to clarify the formalism for the students. Through developing their simulators, students are exposed to the data structure and algorithms to handle the formalism. Consequently, students have the opportunity to make the concept concrete.

Natural languages and the chomsky hierarchy

Abstract: The central claim of the paper is that NL stringsets are regular. Three independent arguments are offered in favor of this position: one based on parsimony considerations, one employing the McCullogh-Pitts (1943) model of neurons, and a purely linguistic one. It is possible to derive explicit upper bounds for the number of (live) states in NL acceptors: the results show that finite state NL parsers can be implemented on present day computers. The position of NL stringsets within the regular family is also investigated: it is proved that NLs are counter-free, but not locally testable.

The Semantics of Cardinality-Based Feature Models via Formal Languages

Abstract: Cardinality-based feature models provide the most expressive language among the existing feature modeling languages. We provide a reduction process, which allows us to transform a cardinality-based feature diagram to an appropriate regular expression. As for crosscutting constraints, we propose a formal language interpretation of them. In this way, we provide a formal language-based semantics for cardinality-based feature models. Accordingly, we describe a computational hierarchy of feature models, which guides us in how feature models can be constructively analyzed. We also characterize some existing analysis operations over feature models in terms of languages and discuss the corresponding decidability problems.

On the Language of Primitive Partial Words

Abstract: A partial word is a word which contains some holes known as do not know symbols and such places can be replaced by any letter from the underlying alphabet We study the relation between language of primitive partial words with the conventional language classes viz regular, linear and deterministic context-free in Chomsky hierarchy We give proofs to show that the language of primitive partial words over an alphabet having at least two letters is not regular, not linear and not deterministic context free language Also we give a 2DPDA automaton that recognizes the language of primitive partial words

Grammatical Inference and Language Frameworks for LANGSEC

Abstract: Formal Language Theory for Security (LANGSEC) has proposed that formal language theory and grammars be used to define and secure protocols and parsers. The assumption is that by restricting languages to lower levels of the Chomsky hierarchy, it is easier to control and verify parser code. In this paper, we investigate an alternative approach to inferring grammars via pattern languages and elementary formal system frameworks. We summarize inferability results for subclasses of both frameworks and discuss how they map to the Chomsky hierarchy. Finally, we present initial results of pattern language learning on logged HTTP sessions and suggest future areas of research.

Formalization of context-free language theory

Abstract: Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related to context-free grammars and languages. These include closure properties (union, concatenation and Kleene star), grammar simplification (elimination of useless symbols inaccessible symbols, empty rules and unit rules) and the existence of a Chomsky Normal Form for context-free grammars.

On side effect machines as a representation for evolutionary algorithms

Abstract: Side Effect Machines (SEMs) have been used as a evolutionary representation in a variety of studies dealing with the classification of data for bioinformatic studies. However, up to this point there has been no formalism of the SEM in terms of its representational ability and placement within the Chomsky hierarchy; only a statement that it is a generalization of a Deterministic Finite Automation (DFA), without proof, has been provided. This paper aims to rectify that situation by presenting a formal look at SEMs in terms of the languages which they are known to accept. We give a constructive proof of how a SEM is a generalization of a DFA and are therefore able to be used to accept languages. Constructive proofs for SEMs accepting families of context-free and context-sensitive languages are also provided.

Finite Automata with Multiset Memory: A New Characterization of Chomsky Hierarchy

Abstract: This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM Finite Automaton with Multiset Memory in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional structural information of stored data. We introduce the class of FAMMs of degree d for non-negative integer d in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

Slavic Languages in the Perspective of Formal Grammar

Abstract: The volume comprises papers that were presented at the 14th European conference on "Formal Description of Slavic Languages" at Masaryk University in Brno, Czech Republic. The conference focuses on formal approaches to Slavic phonology, morphology, syntax and semantics. The present contributions describe interesting data patterns found in Slavic languages and analyze them from the perspective of formal grammar, including generative syntax, Distributed Morphology, formal semantics and others.