---
_id: '10630'
abstract:
- lang: eng
text: In the Intersection Non-emptiness problem, we are given a list of finite automata
A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine
whether some string w ∈ Σ^* lies in the intersection of the languages accepted
by the automata in the list. We analyze the complexity of the Intersection Non-emptiness
problem under the promise that all input automata accept a language in some level
of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy.
Automata accepting languages from the lowest levels of these hierarchies arise
naturally in the context of model checking. We identify a dichotomy in the dot-depth
hierarchy by showing that the problem is already NP-complete when all input automata
accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all
automata accept a language from the level B_1. Conversely, we identify a tetrachotomy
in the Straubing-Thérien hierarchy. More precisely, we show that the problem is
in AC^0 when restricted to level L_0; complete for L or NL, depending on the input
representation, when restricted to languages in the level L_{1/2}; NP-complete
when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally,
PSPACE-complete when the input automata accept languages in level L_2 or higher.
Moreover, we show that the proof technique used to show containment in NP for
DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context
of NFAs. To prove this, we identify a family of languages that provide an exponential
separation between the state complexity of general NFAs and that of partially
ordered NFAs. To the best of our knowledge, this is the first superpolynomial
separation between these two models of computation.
acknowledgement: "We like to thank Lukas Fleischer and Michael Wehar for our discussions.
This work started at the Schloss Dagstuhl Event 20483 Moderne Aspekte der Komplexitätstheorie
in der Automatentheorie https://www.dagstuhl.de/20483.\r\n"
alternative_title:
- LIPIcs
article_number: '34'
article_processing_charge: No
author:
- first_name: Emmanuel
full_name: Arrighi, Emmanuel
last_name: Arrighi
- first_name: Henning
full_name: Fernau, Henning
last_name: Fernau
- first_name: Stefan
full_name: Hoffmann, Stefan
last_name: Hoffmann
- first_name: Markus
full_name: Holzer, Markus
last_name: Holzer
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Mateus
full_name: De Oliveira Oliveira, Mateus
last_name: De Oliveira Oliveira
- first_name: Petra
full_name: Wolf, Petra
last_name: Wolf
citation:
ama: 'Arrighi E, Fernau H, Hoffmann S, et al. On the complexity of intersection
non-emptiness for star-free language classes. In: 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science. Vol
213. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.FSTTCS.2021.34'
apa: 'Arrighi, E., Fernau, H., Hoffmann, S., Holzer, M., Jecker, I. R., De Oliveira
Oliveira, M., & Wolf, P. (2021). On the complexity of intersection non-emptiness
for star-free language classes. In 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science (Vol. 213). Virtual:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34'
chicago: Arrighi, Emmanuel, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismael
R Jecker, Mateus De Oliveira Oliveira, and Petra Wolf. “On the Complexity of Intersection
Non-Emptiness for Star-Free Language Classes.” In 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science, Vol.
213. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34.
ieee: E. Arrighi et al., “On the complexity of intersection non-emptiness
for star-free language classes,” in 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, Virtual, 2021, vol.
213.
ista: 'Arrighi E, Fernau H, Hoffmann S, Holzer M, Jecker IR, De Oliveira Oliveira
M, Wolf P. 2021. On the complexity of intersection non-emptiness for star-free
language classes. 41st IARCS Annual Conference on Foundations of Software Technology
and Theoretical Computer Science. FSTTCS: Foundations of Software Technology and
Theoretical Computer Science, LIPIcs, vol. 213, 34.'
mla: Arrighi, Emmanuel, et al. “On the Complexity of Intersection Non-Emptiness
for Star-Free Language Classes.” 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, vol. 213, 34, Schloss
Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.FSTTCS.2021.34.
short: E. Arrighi, H. Fernau, S. Hoffmann, M. Holzer, I.R. Jecker, M. De Oliveira
Oliveira, P. Wolf, in:, 41st IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz Zentrum
für Informatik, 2021.
conference:
end_date: 2021-12-17
location: Virtual
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2021-12-15
date_created: 2022-01-16T23:01:29Z
date_published: 2021-11-29T00:00:00Z
date_updated: 2022-01-17T10:56:19Z
day: '29'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2021.34
ec_funded: 1
external_id:
arxiv:
- '2110.01279'
file:
- access_level: open_access
checksum: d5a82ba893c3bc5da5914edbb3efb92b
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-17T10:49:03Z
date_updated: 2022-01-17T10:49:03Z
file_id: '10634'
file_name: 2021_LIPIcs_Arrighi.pdf
file_size: 844224
relation: main_file
success: 1
file_date_updated: 2022-01-17T10:49:03Z
has_accepted_license: '1'
intvolume: ' 213'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 41st IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science
publication_identifier:
isbn:
- 978-3-9597-7215-0
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the complexity of intersection non-emptiness for star-free language classes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 213
year: '2021'
...