We are happy to announce that the following article has been accepted
at Application and Theory of Petri Nets and Concurrency (PETRI NETS):
A Myhill-Nerode Theorem for Higher-Dimensional Automata
Uli Fahrenberg, Krzysztof Ziemiański
Abstract: We establish a Myhill-Nerode type theorem for
higher-dimensional automata (HDAs), stating that a language is regular
precisely 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.
The paper is available at
https://arxiv.org/abs/2210.08298