Inductive certification of computed k-abelian complexities

Develop an inductive procedure that, given automata or linear representations produced by the authors’ methods, certifies the correctness of the computed k-abelian complexity functions for general sequences beyond the few cases manually verified.

Background

The authors describe a validation strategy using first-order predicates in Walnut to check large DFAOs, and they successfully verified the Tribonacci DFAO for the balance function and cross-checked some computed k-abelian complexities.

They ask for a more systematic, inductive method to certify results broadly, which would strengthen confidence in large-scale automated computations of generalized abelian complexities.