Weighted HOM-Problem for Nonnegative Integers

TL;DR

This paper proves that it is decidable in polynomial time whether the image of a regular N-weighted tree language remains regular under a nondeleting, nonerasing tree homomorphism, extending the classical HOM-problem.

Contribution

It introduces the N-weighted HOM-problem and establishes its polynomial-time decidability for nondeleting, nonerasing tree homomorphisms.

Findings

Decidability of the N-weighted HOM-problem in polynomial time

Extension of classical HOM-problem to weighted tree languages

Algorithmic framework for weighted tree language transformations

Abstract

The HOM-problem asks whether the image of a regular tree language under a given tree homomorphism is again regular. It was recently shown to be decidable by Godoy, Gim\'enez, Ramos, and \`Alvarez. In this paper, the N-weighted version of this problem is considered and its decidability is proved. More precisely, it is decidable in polynomial time whether the image of a regular N-weighted tree language under a nondeleting, nonerasing tree homomorphism is regular.