Detecting and Explaining (In-)equivalence of Context-Free Grammars
This provides a practical tool for educational support systems to analyze grammar equivalence, though it is incremental as it builds on existing undecidability theory.
The authors tackled the undecidable problem of context-free grammar equivalence by developing a scalable framework that combines multiple techniques, achieving practical performance on large educational datasets where it could handle a substantial portion of cases.
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.