Why the equivalence problem for unambiguous grammars has not been solved back in 1966?

TL;DR

This paper examines the longstanding open problem of determining the equivalence of unambiguous grammars, explaining why earlier proposed methods have not led to a complete solution since 1966.

Contribution

It clarifies the limitations of Semenov's 1966 algorithm based on power series, demonstrating why the equivalence problem remains unsolved.

Findings

Semenov's 1966 algorithm cannot be extended to solve the full equivalence problem.

The equivalence problem for unambiguous grammars remains unresolved due to fundamental limitations.

The paper provides insights into the complexity of grammar equivalence issues.

Abstract

In 1966, Semenov, by using a technique based on power series, suggested an algorithm that tells apart the languages described by an unambiguous grammar and a DFA. At the first glance, it may appear that the algorithm can be easily modified to yield a full solution of the equivalence problem for unambiguous grammars. This article shows why this hunch is, in fact, incorrect.