Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning

Petri net controlled grammars

Different types of regulated grammars have been introduced in order to supplement shortcomings of context-free grammars in applications preserving their elegant mathematical properties. However, the rapid developments in present day industry, biology, and other areas challenge to deal with various tasks which need suitable tools for their modelling and investigation. We propose Petri net controlled grammars as models for representing and analyzing of metabolic pathways in living cells where Petri nets are responsible for the structure and communication of the pathways, and grammars represent biochemical processes. On the other hand, the control by Petri nets has also theoretical interest: it extends possibilities to introduce and investigate concurrent control mechanisms in formal language theory. The thesis introduces various variants of Petri net controlled grammars using different types of Petri nets and investigates their mathematical properties such as computational power and closure properties.Los diferentes tipos de gramáticas con reescritura regulada han sido introducidas para complementar las deficiencias de las gramáticas libres del contexto en las aplicaciones, preservando sus propiedades matemáticas. Por otro lado, la rápida evolución la biología, y otras áreas actuales supone un reto para tratar de las tareas varias que necesitan las herramientas adecuadas para la elaboración de modelos e investigación. Proponemos gramáticas controladas por redes de Petri como modelos para representar y analizar los procesos bioquímicos en las células vivas donde redes de Petri son responsables de la estructura, y gramáticas representan los procesos generativos. Además, el control de redes de Petri también tiene interés teórico: amplía las posibilidades de investigar los mecanismos de control concurrente en la teoría de lenguajes formales. La tesis presenta distintas variantes de gramáticas controladas por redes de Petri e investiga sus propiedades matemáticas

On Descriptive Complexity, Language Complexity, and GB

We introduce $L^2_{K,P}$, a monadic second-order language for reasoning about trees which characterizes the strongly Context-Free Languages in the sense that a set of finite trees is definable in $L^2_{K,P}$ iff it is (modulo a projection) a Local Set---the set of derivation trees generated by a CFG. This provides a flexible approach to establishing language-theoretic complexity results for formalisms that are based on systems of well-formedness constraints on trees. We demonstrate this technique by sketching two such results for Government and Binding Theory. First, we show that {\em free-indexation\/}, the mechanism assumed to mediate a variety of agreement and binding relationships in GB, is not definable in $L^2_{K,P}$ and therefore not enforcible by CFGs. Second, we show how, in spite of this limitation, a reasonably complete GB account of English can be defined in $L^2_{K,P}$. Consequently, the language licensed by that account is strongly context-free. We illustrate some of the issues involved in establishing this result by looking at the definition, in $L^2_{K,P}$, of chains. The limitations of this definition provide some insight into the types of natural linguistic principles that correspond to higher levels of language complexity. We close with some speculation on the possible significance of these results for generative linguistics.Comment: To appear in Specifying Syntactic Structures, papers from the Logic, Structures, and Syntax workshop, Amsterdam, Sept. 1994. LaTeX source with nine included postscript figure

Linguistics and some aspects of its underlying dynamics

In recent years, central components of a new approach to linguistics, the Minimalist Program (MP) have come closer to physics. Features of the Minimalist Program, such as the unconstrained nature of recursive Merge, the operation of the Labeling Algorithm that only operates at the interface of Narrow Syntax with the Conceptual-Intentional and the Sensory-Motor interfaces, the difference between pronounced and un-pronounced copies of elements in a sentence and the build-up of the Fibonacci sequence in the syntactic derivation of sentence structures, are directly accessible to representation in terms of algebraic formalism. Although in our scheme linguistic structures are classical ones, we find that an interesting and productive isomorphism can be established between the MP structure, algebraic structures and many-body field theory opening new avenues of inquiry on the dynamics underlying some central aspects of linguistics.Comment: 17 page