Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

State Complexity of Combined Operations on Finite Languages

State complexity is a descriptive complexity measure for regular languages. It is a fundamental topic in automata and formal language theory. The state complexity of a regular language is the number of states in the minimal complete deterministic finite automaton accepting the language. During the last few decades, many publications have focused and studied the state complexity of many individual as well as combined operations on regular languages. Also, the state complexity of some basic operations on finite languages has been studied. But until now there has been no study on the state complexity of combined operations on finite languages. In this thesis, we will first study the state complexity of the combined operation, star of union, on finite languages and give an exact bound. Then we will investigate the state complexity of star of catenation and show its approximation with a good ratio bound and finally, we will prove an upper bound for star of intersection

Concepts, Frames and Cascades in Semantics, Cognition and Ontology

This open access book presents novel theoretical, empirical and experimental work exploring the nature of mental representations that support natural language production and understanding, and other manifestations of cognition. One fundamental question raised in the text is whether requisite knowledge structures can be adequately modeled by means of a uniform representational format, and if so, what exactly is its nature. Frames are a key topic covered which have had a strong impact on the exploration of knowledge representations in artificial intelligence, psychology and linguistics; cascades are a novel development in frame theory. Other key subject areas explored are: concepts and categorization, the experimental investigation of mental representation, as well as cognitive analysis in semantics. This book is of interest to students, researchers, and professionals working on cognition in the fields of linguistics, philosophy, and psychology

Attributes of Attribution

Attributive adjectives have a number of properties that distinguish them from predicative adjectives and other modifiers of the noun. For example, attributives are subject to ordering restrictions that do not apply to other types of nominal modifier, and they exhibit scope interactions unlike predicatives or relative clauses. This thesis argues that these properties are best captured by an analysis in which all attributives share the same relationship with the noun and discusses the ways in which our understanding of a number of phenomena at the edges of attribution must change. One influential theory of adjective ordering restrictions (discussed in Larson 2000a and Cinque 2010, among others) holds that violations of the ordering hierarchy that applies to many attributive adjectives are due to the existence of modifiers that superficially look like attributives but are in fact derived from reduced relative clauses. These derived attributives are merged higher than underived attributives and are unordered with respect to each other. I show that the offending adjectives do not behave syntactically like true relative clauses, whether full or reduced. In addition, while all attributive semantics is asymmetric, true relatives involve symmetric modification. This single-source approach entails a rethinking of some of the effects commonly understood to result from attribution. I will address two such effects, which could be taken as evidence in favour of a derived attributive approach to attribution, and show that they are best analyzed using a homogeneous approach to attribution. In languages where the noun follows its modifiers, the ordering of AP and PP modifiers is free and their scope varies with c-command. In noun-initial languages their order is fixed, with the AP preceding other modifiers, and their scope is ambiguous. This pattern could be taken as evidence for a second source of adnominal modification, if the high position of the AP in noun-final languages is a reduced relative clause. However, I show that both the ordering and scope effects are due to a novel constraint restricting the linear order of attributive and other modifiers. The ordering patterns of AP and PP modifiers are therefore not evidence for the existence of derived attributives. One piece of evidence for the dual-source theory of attribution is that some adjectives have unexpectedly rigid requirements for adjacency and nonintersectivity (for example, in the phrase hard worker). I demonstrate that cases like these are not true attribution but are instead a type of bracketing paradox. I argue that these bracketing paradoxes are derived by movement at LF. This movement (and indeed all movement) is restricted in the type of information that must be retained before and after the operation takes place, but is other- wise free. Therefore, these examples do not provide evidence for two different types of attributive modifier. The proposed analysis of attribution allows for a simplification of adjectival modification, as it does not require a distinction between derived and underived attributive adjectives. The analysis presented in this thesis entails a novel categorization of certain adjectival phenomena, but readily accounts for the empirical intricacies of attribution

Roots of language

Roots of language was originally published in 1981 by Karoma Press (Ann Arbor). It was the first work to systematically develop a theory first suggested by Coelho in the late nineteenth century: that the creation of creole languages somehow reflected universal properties of language. The book also proposed that the same set of properties would be found to emerge in normal first-language acquisition and must have emerged in the original evolution of language. These proposals, some of which were elaborated in an article in Behavioral and Brain Sciences (1984), were immediately controversial and gave rise to a great deal of subsequent research in creoles, much of it aimed at rebutting the theory. The book also served to legitimize and stimulate research in language evolution, a topic regarded as off-limits by linguists for over a century. The present edition contains a foreword by the author bringing the theory up to date; a fuller exposition of many of its aspects can be found in the author’s most recent work, More than nature needs (Harvard University Press, 2014)

Roots of language

Roots of language was originally published in 1981 by Karoma Press (Ann Arbor). It was the first work to systematically develop a theory first suggested by Coelho in the late nineteenth century: that the creation of creole languages somehow reflected universal properties of language. The book also proposed that the same set of properties would be found to emerge in normal first-language acquisition and must have emerged in the original evolution of language. These proposals, some of which were elaborated in an article in Behavioral and Brain Sciences (1984), were immediately controversial and gave rise to a great deal of subsequent research in creoles, much of it aimed at rebutting the theory. The book also served to legitimize and stimulate research in language evolution, a topic regarded as off-limits by linguists for over a century. The present edition contains a foreword by the author bringing the theory up to date; a fuller exposition of many of its aspects can be found in the author’s most recent work, More than nature needs (Harvard University Press, 2014)

Roots of language

Roots of language was originally published in 1981 by Karoma Press (Ann Arbor). It was the first work to systematically develop a theory first suggested by Coelho in the late nineteenth century: that the creation of creole languages somehow reflected universal properties of language. The book also proposed that the same set of properties would be found to emerge in normal first-language acquisition and must have emerged in the original evolution of language. These proposals, some of which were elaborated in an article in Behavioral and Brain Sciences (1984), were immediately controversial and gave rise to a great deal of subsequent research in creoles, much of it aimed at rebutting the theory. The book also served to legitimize and stimulate research in language evolution, a topic regarded as off-limits by linguists for over a century. The present edition contains a foreword by the author bringing the theory up to date; a fuller exposition of many of its aspects can be found in the author’s most recent work, More than nature needs (Harvard University Press, 2014)

Roots of language

Roots of language was originally published in 1981 by Karoma Press (Ann Arbor). It was the first work to systematically develop a theory first suggested by Coelho in the late nineteenth century: that the creation of creole languages somehow reflected universal properties of language. The book also proposed that the same set of properties would be found to emerge in normal first-language acquisition and must have emerged in the original evolution of language. These proposals, some of which were elaborated in an article in Behavioral and Brain Sciences (1984), were immediately controversial and gave rise to a great deal of subsequent research in creoles, much of it aimed at rebutting the theory. The book also served to legitimize and stimulate research in language evolution, a topic regarded as off-limits by linguists for over a century. The present edition contains a foreword by the author bringing the theory up to date; a fuller exposition of many of its aspects can be found in the author’s most recent work, More than nature needs (Harvard University Press, 2014)