Myhill-Nerode Theorem for Higher-Dimensional Automata
Uli Fahrenberg, Krzysztof Ziemia\'nski
TL;DR
This paper extends the Myhill-Nerode theorem to higher-dimensional automata, characterizing regular languages via finite prefix quotients and exploring determinization limitations.
Contribution
It introduces a Myhill-Nerode theorem for HDAs, defines deterministic HDAs, and analyzes their recognizability and determinization properties.
Findings
A Myhill-Nerode theorem for HDAs is established.
Not all regular languages are recognizable by deterministic HDAs.
An internal characterization of deterministic languages is developed.
Abstract
We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible to distinguish between interleavings and concurrency. We also introduce deterministic HDAs and show that not all HDAs are determinizable, that is, there exist regular languages that cannot be recognised by a deterministic HDA. Using our theorem, we develop an internal characterisation of deterministic languages. Lastly, we develop analogues of the Myhill-Nerode construction and of determinacy for HDAs with interfaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.