Separability and Non-Determinizability of WSTS

Abstract

We study the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that every pair of disjoint WSTS languages is regularly separable: there is a regular language containing one of them while being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. Our second result shows that the languages recognized by deterministic WSTS form a strict subclass of the languages recognized by all WSTS: we give a non-deterministic WSTS language that we prove cannot be recognized by a deterministic WSTS. The proof relies on a novel characterization of the languages accepted by deterministic WSTS.

This paper is the journal version of the CONCUR23 paper "Separability and Non-Determinizability of WSTS'', which can be found in the previous version of this arxiv document. It covers both papers about regular separability in WSTS: the CONCUR23 paper and its predecessor the CONCUR18 paper. As this version does not contain an appendix, please refer to the previous version for missing proofs