A Note on the Complexity of Restricted Attribute-Value Grammars

TL;DR

This paper investigates a restricted form of attribute-value grammars (R-AVG), showing it can recognize all context-free languages and more, with a decidable but NP-complete recognition problem, and introduces a new constraint linking R-AVG to complexity classes.

Contribution

It introduces R-AVG, a restricted, decidable form of AVGs that captures all context-free languages and relates to complexity classes via a new parsability constraint.

Findings

R-AVG captures all context-free languages and more

Recognition problem for R-AVG is decidable but NP-complete

Honest parsability constraint links R-AVG to complexity classes

Abstract

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.