Deterministic and game separability for regular languages of infinite trees

TL;DR

This paper proves that it is decidable whether two regular languages of infinite trees can be separated by a deterministic or game language, with complexity bounds and automata size considerations.

Contribution

It introduces decidability results for separability of infinite tree languages by deterministic and game languages, including complexity and automata size bounds.

Findings

Decidability of separability in EXPTIME

Separating automata of exponential size are sufficient

Reduction to infinite duration games with -regular conditions

Abstract

We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the separator is fixed, or not. In each case, we show that separability can be decided in EXPTIME, and that separating automata of exponential size suffice. We obtain our results by reducing to infinite duration games with {\omega}-regular winning conditions and applying the finite-memory determinacy theorem of B\"uchi and Landweber.