A Myhill-Nerode Theorem for Higher-Dimensional Automata
From LRDE
- Authors
- Uli Fahrenberg, Krzysztof Ziemiański
- Where
- Application and Theory of Petri Nets and Concurrency (PETRI NETS)
- Type
- inproceedings
- Publisher
- Springer
- Projects
- AA"AA" is not in the list (Vaucanson, Spot, URBI, Olena, APMC, Tiger, Climb, Speaker ID, Transformers, Bison, ...) of allowed values for the "Related project" property.
- Date
- 2023-03-05
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.
Bibtex (lrde.bib)
@InProceedings{ fahrenberg.23.pn, author = {Fahrenberg, Uli and Ziemia{\'n}ski, Krzysztof}, title = {A {Myhill}-{Nerode} Theorem for Higher-Dimensional Automata}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, booktitle = {Application and Theory of Petri Nets and Concurrency (PETRI NETS)}, year = {2023}, doi = {FIXME}, 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.}, month = mar, note = {Accepted} }