The Power of Constraint Grammars Revisited

TL;DR

This paper explores the formal language theory connections of Sequential Constraint Grammar (SCG), demonstrating its computational limits, undecidability, and conditions under which it can be represented as a finite-state transducer.

Contribution

It establishes formal language theoretical foundations for SCG, including undecidability results and finite-state conditions, advancing understanding of its computational properties.

Findings

Nonmonotonic SCG is undecidable.

Resource bounds restrict SCG to a subset of context-sensitive languages.

Finite-state transducer equivalence under specific time constraints.

Abstract

Sequential Constraint Grammar (SCG) (Karlsson, 1990) and its extensions have lacked clear connections to formal language theory. The purpose of this article is to lay a foundation for these connections by simplifying the definition of strings processed by the grammar and by showing that Nonmonotonic SCG is undecidable and that derivations similar to the Generative Phonology exist. The current investigations propose resource bounds that restrict the generative power of SCG to a subset of context sensitive languages and present a strong finite-state condition for grammars as wholes. We show that a grammar is equivalent to a finite-state transducer if it is implemented with a Turing machine that runs in o(n log n) time. This condition opens new finite-state hypotheses and avenues for deeper analysis of SCG instances in the way inspired by Finite-State Phonology.