Detecting and Explaining (In-)equivalence of Context-Free Grammars

TL;DR

This paper introduces a scalable framework for deciding, proving, and explaining the (in-)equivalence of context-free grammars, with practical implementation and evaluation on educational datasets.

Contribution

It combines multiple techniques, including grammar transformation, theory-based comparison, and graph canonization, to handle large datasets despite the undecidability of the general problem.

Findings

Framework handles a large portion of datasets effectively.

Combines multiple techniques for grammar comparison.

Successfully evaluated on educational support system data.

Abstract

We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems. Even though the equivalence problem for context-free languages is undecidable in general, the framework is able to handle a large portion of these datasets. It introduces and combines techniques from several areas, such as an abstract grammar transformation language to identify equivalent grammars as well as sufficiently similar inequivalent grammars, theory-based comparison algorithms for a large class of context-free languages, and a graph-theory-inspired grammar canonization that allows to efficiently identify isomorphic grammars.