The FC-rank of a context-free language

TL;DR

This paper proves that the FC-rank of the lexicographic ordering of any context-free language is always less than 5^55, establishing an upper bound for this measure.

Contribution

It establishes a universal upper bound on the FC-rank of lexicographic orderings of all context-free languages, advancing understanding of their structural complexity.

Findings

FC-rank of context-free language lexicographic orderings is less than 5^55

Provides a bound that applies universally to all such languages

Enhances understanding of the complexity of language orderings

Abstract

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than $\omega^\omega$.