Characterizing Formality

Complexity classes are defined by quantitative restrictions of resources available to a computational model, like for instance the Turing machine. Contrarily, there is no obvious commonality in the definition of families of formal languages - instead they are described by example. This thesis is about the characterization of what makes a set of languages a family of formal languages. Families of formal languages, like for example the regular, context-free languages and their sub-families exhibit properties that are contrasted by the ones of complexity classes. Two of the properties families of formal languages seem to have is closure of intersection with regular languages, another is the existence of pumping or iteration arguments which yield the decidability of the emptiness. Complexity classes do not generally have a decidable emptiness, which lead us to a first candidate for the notion of formality - the decidability of the emptiness of regular intersection (intreg). We refute the decidability of intreg as a criterion by hiding the difficulty of deciding the emptiness of regular intersection: We show that for every decidable language L there is a language L' of essentially the same complexity such that intreg(L') is decidable. This implies that every complexity class contains complete languages for which the emptiness of regular intersection is decidable. An intermediate result we show is that the set of true quantified Boolean formulae has a decidable emptiness of regular intersection. As the known families of formal languages are all contained in NP, this yields a language (probably) outside of NP for which intreg is decidable, which additionally is a natural language in contrast to the artificial ones obtained by the hiding process. We introduce the notion of protocol languages which capture in some sense the behavior of a data-structure underlying the model of a formal language. They are defined in a fragment of second order logic, where the second order variables are uniquely determined by each word in the language and each letter implies a determined sub-structure of a word. Viewing the letters of a word as vertices and the successor as edges between them, each word can be seen as a path. The binary second order variables can be viewed as additional edges between word positions. Therefore, each word in a protocol language defines some unique graph. These graphs can be recognized by covering them with a predefined set of tiles which are node and edge-labeld graphs. Additional numerical constraints on the amount of each tile-type yields shrinking-arguments for protocol languages. If a word w in a protocol language exceeds a certain length such that the numerical constraints are (over-)satisfied, one can constuctively generate a shorter word w' from w that is also contained in the protocol language. We define logical extensions of protocol languages by allowing the conjunction of additional first order or monadic second order definable formulae and analyze the extensions in regard to trio operations. Protocol languages for the regular, context-free and indexed languages are exhibited -- for the first two we give protocol languages which act as generators for the respective family of formal languages. Finally, we show that the emptiness of protocol languages is decidable

Parsing Strategies With \u27Lexicalized\u27 Grammars: Application to Tree Adjoining Grammars

In this paper, we present a parsing strategy that arose from the development of an Earley-type parsing algorithm for TAGs (Schabes and Joshi 1988) and from some recent linguistic work in TAGs (Abeillé: 1988a). In our approach, each elementary structure is systematically associated with a lexical head. These structures specify extended domains of locality (as compared to a context-free grammar) over which constraints can be stated. These constraints either hold within the elementary structure itself or specify what other structures can be composed with a given elementary structure. The \u27grammar\u27 consists of a lexicon where each lexical item is associated with a finite number of structures for which that item is the head. There are no separate grammar rules. There are, of course, \u27rules\u27 which tell us how these structures are composed. A grammar of this form will be said to be \u27lexicalized\u27. We show that in general context-free grammars cannot be \u27lexicalized\u27. We then show how a \u27lexicalized\u27 grammar naturally follows from the extended domain of locality of TAGs and examine briefly some of the linguistic implications of our approach. A general parsing strategy for \u27lexicalized\u27 grammars is discussed. In the first stage, the parser selects a set of elementary structures associated with the lexical items in the input sentence, and in the second stage the sentence is parsed with respect to this set. The strategy is independent of nature of the elementary structures in the underlying grammar. However, we focus our attention on TAGs. Since the set of trees selected at the end of the first stage is not infinite, the parser can use in principle any search strategy. Thus, in particular, a top-down strategy can be used since problems due to recursive structures are eliminated. We then explain how the Earley-type parser for TAGs can be modified to take advantage of this approach

On Folding and Twisting (and whatknot): towards a characterization of workspaces in syntax

Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete recursive combinatorics over lexical items which get assembled into phrases, which are themselves combined to form sentences. This view is common to European and American structuralism (e.g., Benveniste, 1971; Hockett, 1958) and different incarnations of generative grammar, transformational and non-transformational (Chomsky, 1956, 1995; and Kaplan & Bresnan, 1982; Gazdar, 1982). Since at least Uriagereka (2002), there has been some attention paid to the fact that syntactic operations must apply somewhere, particularly when copying and movement operations are considered. Contemporary syntactic theory has thus somewhat acknowledged the importance of formalizing aspects of the spaces in which elements are manipulated, but it is still a vastly underexplored area. In this paper we explore the consequences of conceptualizing syntax as a set of topological operations applying over spaces rather than over discrete elements. We argue that there are empirical advantages in such a view for the treatment of long-distance dependencies and cross-derivational dependencies: constraints on possible configurations emerge from the dynamics of the system.Comment: Manuscript. Do not cite without permission. Comments welcom

New Results on Context-Free Tree Languages

Context-free tree languages play an important role in algebraic semantics and are applied in mathematical linguistics. In this thesis, we present some new results on context-free tree languages

The pragmatic formalization of computing systems relative to a given high-level language

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