Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

(ML)2: A Formal Language for KADS Models.

Abstract: Abstract This paper reports on an investigation into a formal language for specifying KADS models of expertise. After arguing the need for and the use of such formal representations, we discuss each of the layers of a KADS model of expertise in the subsequent sections, and define the formal constructions that we use to represent the KADS entities at every layer: order-sorted logic at the domain layer, meta-logic at the inference layer and dynamic-logic at the task layer. All these constructions together make up (ML)2, the language that we use to represent models of expertise. We illustrate the use of (ML)2 in a small example model. We conclude by describing our experience to date with constructing such formal models in (ML)2, and by discussing some open problems that remain for future work.

An Optimal Control Theory for Discrete Event Systems

Abstract: In certain discrete event applications it may be desirable to find a particular controller, within the set of acceptable controllers, which optimizes some quantitative performance measure. In this paper we propose a theory of optimal control to meet such design requirements for deterministic systems. The discrete event system (DES) is modeled by a formal language. Event and cost functions are defined which induce costs on controlled system behavior. The event costs associated with the system behavior can be reduced, in general, only by increasing the control costs. Thus it is nontrivial to find the optimal amount of control to use, and the formulation captures the fundamental tradeoff motivating classical optimal control. Results on the existence of minimally restrictive optimal solutions are presented. Communication protocols are analyzed to motivate the formulation and demonstrate optimal controller synthesis. Algorithms for the computation of optimal controllers are developed for the special case of DES modeled by regular languages. It is shown that this framework generalizes some of the existing literature.

Finiteness and Regularity in Semigroups and Formal Languages

Abstract: This is a rigorous and self-contained monograph on a central topic in theoretical computer science. For the first time in book form, original results from the last ten years are presented, some previously unpublished, using combinatorial and algebraic methods. These are mainly based on combinatorics on words and especially on the theory of "unavoidable regularities." Researchers will find important new results on semigroups and formal languages, as well as various applications for these methods.

Formal and computational aspects of natural language syntax

Abstract: This thesis explores issues related to using a restricted mathematical formalism as the formal basis for the representation of syntactic competence and the modeling of performance. The specific contribution of this thesis is to examine a language with considerably freer word-order than English, namely German, and to investigate the formal requirements that this syntactic freedom imposes. The formal systems investigated in this thesis are based on the tree adjoining grammar (TAG) formalism of Joshi et al. (1975). TAG is an appealing formalism for the representation of natural language syntax because its elementary structures are trees, which allows the linguist to localize linguistic dependencies such as agreement, subcategorization, and filler-gap relations, and to develop a theory of grammar based on the lexicon. The main results of the thesis are an argument that simple TAGs are formally inadequate, and the definition of an extension to TAG that is. Every aspect of the definition of this extension to TAG, called V-TAG, is specifically motivated by linguistic facts, not by formal considerations. A formal investigation of V-TAG reveals that (when lexicalized) it has restricted generative capacity, that it is polynomial parsable, and that it forms an abstract family of languages. This means that it has desirable formal properties for representing natural language syntax. Both a formal automaton and a parser for V-TAG are presented. As a consequence of the new system, a reformulation of the linguistic theory that has been proposed for TAG suggests itself. Instead of including a transformational step in the theory of grammar, all derivations are performed within mathematically defined formalisms, thus limiting the degrees of freedom in the linguistic theory, and making the theory more appealing from a computational point of view. The thesis sketches a fragment of a grammar of German, which covers phenomena such as scrambling, extraposition, topicalization, and the V2 effect. Finally, the formal automaton for V-TAG is used as a model of human syntactic processing. It is shown that this model makes several interesting predictions related to free word order in German.

Automata and Languages: Theory and Applications

Abstract: I Introduction.- Mathematical Background.- 1 Languages.- 2 Automata.- II Regular Languages.- 3 Models for Regular Languages.- 4 Properties of Regular Languages.- III Context-Free Languages.- 5 Models for Context-Free Languages.- 6 Properties of Context-Free Languages.- 7 Special Types of Context-Free Languages and Their Models.- IV Beyond Context-Free Languages.- 8 Generalized Models.- V Translations.- 9 Finite and Pushdown Transducers.- 10 Turing Transducers.- Indices.- Index to Special Symbols.- Index to Decision Problems.- Index to Algorithms.