Decision problems for Clark-congruential languages

TL;DR

This paper proves that the equivalence problem for Clark-congruential grammars is decidable and also provides a method to check whether a given CFG belongs to this class, which is relevant for grammatical inference.

Contribution

It establishes the decidability of equivalence and membership problems for Clark-congruential grammars, advancing understanding in grammatical inference.

Findings

Equivalence for Clark-congruential grammars is decidable.

Membership checking for DCFGs is decidable.

Clark-congruential grammars are significant in grammatical inference.

Abstract

A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a DCFG.