Splicing systems and the Chomsky hierarchy

In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature

Taking Primitive Optimality Theory Beyond the Finite State

Primitive Optimality Theory (OTP) (Eisner, 1997a; Albro, 1998), a computational model of Optimality Theory (Prince and Smolensky, 1993), employs a finite state machine to represent the set of active candidates at each stage of an Optimality Theoretic derivation, as well as weighted finite state machines to represent the constraints themselves. For some purposes, however, it would be convenient if the set of candidates were limited by some set of criteria capable of being described only in a higher-level grammar formalism, such as a Context Free Grammar, a Context Sensitive Grammar, or a Multiple Context Free Grammar (Seki et al., 1991). Examples include reduplication and phrasal stress models. Here we introduce a mechanism for OTP-like Optimality Theory in which the constraints remain weighted finite state machines, but sets of candidates are represented by higher-level grammars. In particular, we use multiple context-free grammars to model reduplication in the manner of Correspondence Theory (McCarthy and Prince, 1995), and develop an extended version of the Earley Algorithm (Earley, 1970) to apply the constraints to a reduplicating candidate set.Comment: 11 pages, 5 figures, worksho

A Case Study of the Convergence of Mildly Context-Sensitive Formalisms for Natural Language Syntax: from Minimalist Grammars to Multiple Context-Free Grammars

Soumis en tant que rapport de recherche INRIA Futurs - Projet SIGNESThe present work is set in the field of natural language syntactic parsing. We present the concept of "mildly context-sensitive" grammar formalisms, which are full-fetched and efficient for syntactic parsing. We summarize a number of these formalisms' definitions, together with the relations between one another, and, most importantly, a survey of known equivalences. The conversion of Edward Stabler's Minimalist Grammars into Multiple Context-Free Grammars (MCFG) is presented in particular detail, along with a study of the complexity of this procedure and of its implications for parsing. This report is an adaptation of the French Master thesis that bears the same name, from Bordeaux 1 University, June 2006

On Pregroups, Freedom, and (Virtual) Conceptual Necessity

Pregroups were introduced in (Lambek, 1999), and provide a founda-tion for a particularly simple syntactic calculus. Buszkowski (2001) showed that free pregroup grammars generate exactly the -free context-free lan-guages. Here we characterize the class of languages generable by all pre-groups, which will be shown to be the entire class of recursively enumerable languages. To show this result, we rely on the well-known representation of recursively enumerable languages as the homomorphic image of the inter-section of two context-free languages (Ginsburg et al., 1967). We define an operation of cross-product over grammars (so-called because of its behaviour on the types), and show that the cross-product of any two free-pregroup grammars generates exactly the intersection of their respective languages. The representation theorem applies once we show that allowing ‘empty cat-egories ’ (i.e. lexical items without overt phonological content) allows us to mimic the effects of any string homomorphism.