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arXiv · 2305.02736

Separability and Non-Determinizability of WSTS

Wojciech Czerwiński·Eren Keskin·Sławomir Lasota·Roland Meyer·Sebastian Muskalla·K Narayan Kumar·Prakash Saivasan
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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.

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Wojciech Czerwiński, Eren Keskin, Sławomir Lasota, Roland Meyer, Sebastian Muskalla, K Narayan Kumar, Prakash Saivasan. 2023-05-04. Separability and Non-Determinizability of WSTS. https://arxiv.org/abs/2305.02736

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