Links between O_N and indexed grammars

Establish further links between the languages O_N and structures independent of multiple context-free grammars, particularly indexed grammars, in order to address the open problems concerning such relationships.

Background

The paper studies the language O_N of balanced words and proves a strengthened multiple-context-free characterization for O_2 using derivation rules with additional factor-length conditions. The conclusion suggests extending this line of inquiry beyond multiple context-free grammars to formalisms such as indexed grammars.

The authors explicitly identify the study of links between O_N and indexed grammars as involving open problems. This is presented as a broader research direction motivated by the paper's strengthened characterization, rather than as a question resolved by the results for O_2.