A Note on the Complexity of Restricted Attribute-Value Grammars

The recognition problem for attribute-value grammars (AVGs) was shown to be undecidable by Johnson in 1988. Therefore, the general form of AVGs is of no practical use. In this paper we study a very restricted form of AVG, for which the recognition problem is decidable (though still NP-complete), the R-AVG. We show that the R-AVG formalism captures all of the context free languages and more, and introduce a variation on the so-called `off-line parsability constraint', the `honest parsability constraint', which lets different types of R-AVG coincide precisely with well-known time complexity classes.Comment: 18 pages, also available by (1) anonymous ftp at ftp://ftp.fwi.uva.nl/pub/theory/illc/researchReports/CT-95-02.ps.gz ; (2) WWW from http://www.fwi.uva.nl/~mtrautwe

On the Mathematical Properties of Linguistic Theories

This paper surveys some of these results and discusses their significance for linguistic theory. However, we will avoid entirely the issue of whether one theory is more descrip- tively adequate than another. We will consider context- free, transformational, lexical-functional, generalized phrase structure, tree adjunct, and stratificational grammars) Although this paper focuses on metatheoretic results as arbiters among theories as models of human linguistic capacities, they may have other uses as well. Complexity results could be utilized for making decisions about the implementation of parsers as components of computerbased language-understanding systems. However, as Stanley Peters has pointed out, no one should underestimate "the pleasure to be derived from ferreting out these results! 3 2. Preliminary Definitions We assume that the reader is familiar with the basic defi- nitions of regular, context-free (CF), context-sensitive (CS), recursive, and recursively enumerable (r.e.) languages, as well as with their acceptors (see Hopcroft and Ullman 1979). We will be much concerned with the problem of recognizing whether a string is contained in a given language (the recognition problem) and with that of 1 This research was sponsored in part by the National Science and Engineering Research Council of Canada under Grant A9285. It was made possible in part by a gift from the Systems Development Foundation. An earlier version of this paper appeared in the Proceedings of the 21st ,4nnual Meeting of the ,4ssociation for Computational Linguistics, Cambridge, MA, June 198