Assessing Complexity Results in Feature Theories

In this paper, we assess the complexity results of formalisms that describe the feature theories used in computational linguistics. We show that from these complexity results no immediate conclusions can be drawn about the complexity of the recognition problem of unification grammars using these feature theories. On the one hand, the complexity of feature theories does not provide an upper bound for the complexity of such unification grammars. On the other hand, the complexity of feature theories need not provide a lower bound. Therefore, we argue for formalisms that describe actual unification grammars instead of feature theories. Thus the complexity results of these formalisms judge upon the hardness of unification grammars in computational linguistics.

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.