# It is undecidable if two regular tree languages can be separated by a deterministic tree-walking automaton

## TL;DR

This paper proves that it is undecidable to determine whether two regular tree languages can be separated by a deterministic tree-walking automaton, highlighting fundamental limits in automata theory.

## Contribution

The paper establishes the undecidability of the separation problem for regular tree languages by deterministic automata, using a novel proof technique.

## Key findings

- Decidability of separation by deterministic tree-walking automata is impossible.
- The proof employs a technique from Kopczyński (2016).
- The result impacts automata theory and formal language classification.

## Abstract

The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of Kopczy\'nski from LICS 2016.