---
_id: '14600'
abstract:
- lang: eng
text: We study the problem of learning controllers for discrete-time non-linear
stochastic dynamical systems with formal reach-avoid guarantees. This work presents
the first method for providing formal reach-avoid guarantees, which combine and
generalize stability and safety guarantees, with a tolerable probability threshold
$p\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine
learning literature and it represents formal certificates as neural networks.
In particular, we learn a certificate in the form of a reach-avoid supermartingale
(RASM), a novel notion that we introduce in this work. Our RASMs provide reachability
and avoidance guarantees by imposing constraints on what can be viewed as a stochastic
extension of level sets of Lyapunov functions for deterministic systems. Our approach
solves several important problems -- it can be used to learn a control policy
from scratch, to verify a reach-avoid specification for a fixed control policy,
or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification.
We validate our approach on $3$ stochastic non-linear reinforcement learning tasks.
article_processing_charge: No
author:
- first_name: Dorde
full_name: Zikelic, Dorde
id: 294AA7A6-F248-11E8-B48F-1D18A9856A87
last_name: Zikelic
orcid: 0000-0002-4681-1699
- first_name: Mathias
full_name: Lechner, Mathias
id: 3DC22916-F248-11E8-B48F-1D18A9856A87
last_name: Lechner
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000-0002-2985-7724
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
citation:
ama: Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies
for stochastic systems with reach-avoid guarantees. arXiv. doi:10.48550/ARXIV.2210.05308
apa: Zikelic, D., Lechner, M., Henzinger, T. A., & Chatterjee, K. (n.d.). Learning
control policies for stochastic systems with reach-avoid guarantees. arXiv.
https://doi.org/10.48550/ARXIV.2210.05308
chicago: Zikelic, Dorde, Mathias Lechner, Thomas A Henzinger, and Krishnendu Chatterjee.
“Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.”
ArXiv, n.d. https://doi.org/10.48550/ARXIV.2210.05308.
ieee: D. Zikelic, M. Lechner, T. A. Henzinger, and K. Chatterjee, “Learning control
policies for stochastic systems with reach-avoid guarantees,” arXiv. .
ista: Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies
for stochastic systems with reach-avoid guarantees. arXiv, 10.48550/ARXIV.2210.05308.
mla: Zikelic, Dorde, et al. “Learning Control Policies for Stochastic Systems with
Reach-Avoid Guarantees.” ArXiv, doi:10.48550/ARXIV.2210.05308.
short: D. Zikelic, M. Lechner, T.A. Henzinger, K. Chatterjee, ArXiv (n.d.).
date_created: 2023-11-24T13:10:09Z
date_published: 2022-11-29T00:00:00Z
date_updated: 2024-01-22T14:08:29Z
day: '29'
department:
- _id: KrCh
- _id: ToHe
doi: 10.48550/ARXIV.2210.05308
ec_funded: 1
external_id:
arxiv:
- '2210.05308'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2210.05308
month: '11'
oa: 1
oa_version: Preprint
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 62781420-2b32-11ec-9570-8d9b63373d4d
call_identifier: H2020
grant_number: '101020093'
name: Vigilant Algorithmic Monitoring of Software
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '14539'
relation: dissertation_contains
status: public
- id: '14830'
relation: later_version
status: public
status: public
title: Learning control policies for stochastic systems with reach-avoid guarantees
tmp:
image: /images/cc_by_sa.png
legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
BY-SA 4.0)
short: CC BY-SA (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2022'
...
---
_id: '10052'
abstract:
- lang: eng
text: "A deterministic finite automaton (DFA) \U0001D49C is composite if its language
L(\U0001D49C) can be decomposed into an intersection ⋂_{i = 1}^k L(\U0001D49C_i)
of languages of smaller DFAs. Otherwise, \U0001D49C is prime. This notion of primality
was introduced by Kupferman and Mosheiff in 2013, and while they proved that we
can decide whether a DFA is composite, the precise complexity of this problem
is still open, with a doubly-exponential gap between the upper and lower bounds.
In this work, we focus on permutation DFAs, i.e., those for which the transition
monoid is a group. We provide an NP algorithm to decide whether a permutation
DFA is composite, and show that the difficulty of this problem comes from the
number of non-accepting states of the instance: we give a fixed-parameter tractable
algorithm with the number of rejecting states as the parameter. Moreover, we investigate
the class of commutative permutation DFAs. Their structural properties allow us
to decide compositionality in NL, and even in LOGSPACE if the alphabet size is
fixed. Despite this low complexity, we show that complex behaviors still arise
in this class: we provide a family of composite DFAs each requiring polynomially
many factors with respect to its size. We also consider the variant of the problem
that asks whether a DFA is k-factor composite, that is, decomposable into k smaller
DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation
DFAs, restricting the number of factors makes the decision computationally harder,
and yields a problem with tight bounds: it is NP-complete. Finally, we show that
in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton
alphabet."
acknowledgement: "Ismaël Jecker: Marie Skłodowska-Curie Grant Agreement No. 754411.
Nicolas Mazzocchi: BOSCO project PGC2018-102210-B-I00 (MCIU/AEI/FEDER, UE), BLOQUESCM
project S2018/TCS-4339, and MINECO grant RYC-2016-20281.\r\nPetra Wolf : DFG project
FE 560/9-1.\r\n"
alternative_title:
- LIPIcs
article_number: '18'
article_processing_charge: No
author:
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Nicolas
full_name: Mazzocchi, Nicolas
last_name: Mazzocchi
- first_name: Petra
full_name: Wolf, Petra
last_name: Wolf
citation:
ama: 'Jecker IR, Mazzocchi N, Wolf P. Decomposing permutation automata. In: 32nd
International Conference on Concurrency Theory. Vol 203. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.CONCUR.2021.18'
apa: 'Jecker, I. R., Mazzocchi, N., & Wolf, P. (2021). Decomposing permutation
automata. In 32nd International Conference on Concurrency Theory (Vol.
203). Paris, France: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2021.18'
chicago: Jecker, Ismael R, Nicolas Mazzocchi, and Petra Wolf. “Decomposing Permutation
Automata.” In 32nd International Conference on Concurrency Theory, Vol.
203. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.CONCUR.2021.18.
ieee: I. R. Jecker, N. Mazzocchi, and P. Wolf, “Decomposing permutation automata,”
in 32nd International Conference on Concurrency Theory, Paris, France,
2021, vol. 203.
ista: 'Jecker IR, Mazzocchi N, Wolf P. 2021. Decomposing permutation automata. 32nd
International Conference on Concurrency Theory. CONCUR: Conference on Concurrency
Theory, LIPIcs, vol. 203, 18.'
mla: Jecker, Ismael R., et al. “Decomposing Permutation Automata.” 32nd International
Conference on Concurrency Theory, vol. 203, 18, Schloss Dagstuhl - Leibniz
Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.CONCUR.2021.18.
short: I.R. Jecker, N. Mazzocchi, P. Wolf, in:, 32nd International Conference on
Concurrency Theory, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-27
location: Paris, France
name: 'CONCUR: Conference on Concurrency Theory'
start_date: 2021-08-23
date_created: 2021-09-27T14:33:14Z
date_published: 2021-08-13T00:00:00Z
date_updated: 2022-05-13T08:12:52Z
day: '13'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.CONCUR.2021.18
ec_funded: 1
external_id:
arxiv:
- '2107.04683'
file:
- access_level: open_access
checksum: 4722c81be82265cf45e78adf9db91250
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T11:10:53Z
date_updated: 2021-10-01T11:10:53Z
file_id: '10064'
file_name: 2021_CONCUR_Jecker.pdf
file_size: 1003552
relation: main_file
success: 1
file_date_updated: 2021-10-01T11:10:53Z
has_accepted_license: '1'
intvolume: ' 203'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 32nd International Conference on Concurrency Theory
publication_identifier:
isbn:
- 978-3-9597-7203-7
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decomposing permutation automata
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2021'
...
---
_id: '10054'
abstract:
- lang: eng
text: 'Graphs and games on graphs are fundamental models for the analysis of reactive
systems, in particular, for model-checking and the synthesis of reactive systems.
The class of ω-regular languages provides a robust specification formalism for
the desired properties of reactive systems. In the classical infinitary formulation
of the liveness part of an ω-regular specification, a "good" event must happen
eventually without any bound between the good events. A stronger notion of liveness
is bounded liveness, which requires that good events happen within d transitions.
Given a graph or a game graph with n vertices, m edges, and a bounded liveness
objective, the previous best-known algorithmic bounds are as follows: (i) O(dm)
for graphs, which in the worst-case is O(n³); and (ii) O(n² d²) for games on graphs.
Our main contributions improve these long-standing algorithmic bounds. For graphs
we present: (i) a randomized algorithm with one-sided error with running time
O(n^{2.5} log n) for the bounded liveness objectives; and (ii) a deterministic
linear-time algorithm for the complement of bounded liveness objectives. For games
on graphs, we present an O(n² d) time algorithm for the bounded liveness objectives.'
acknowledgement: 'Krishnendu Chatterjee: Supported by the ERC CoG 863818 (ForM-SMArt).
Monika Henzinger: Supported by the Austrian Science Fund (FWF) and netIDEE SCIENCE
project P 33775-N. Sagar Sudhir Kale: Partially supported by the Vienna Science
and Technology Fund (WWTF) through project ICT15-003. Alexander Svozil: Fully supported
by the Vienna Science and Technology Fund (WWTF) through project ICT15-003.'
alternative_title:
- LIPIcs
article_number: '124'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Sagar Sudhir
full_name: Kale, Sagar Sudhir
last_name: Kale
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Henzinger MH, Kale SS, Svozil A. Faster algorithms for bounded
liveness in graphs and game graphs. In: 48th International Colloquium on Automata,
Languages, and Programming. Vol 198. Schloss Dagstuhl - Leibniz Zentrum für
Informatik; 2021. doi:10.4230/LIPIcs.ICALP.2021.124'
apa: 'Chatterjee, K., Henzinger, M. H., Kale, S. S., & Svozil, A. (2021). Faster
algorithms for bounded liveness in graphs and game graphs. In 48th International
Colloquium on Automata, Languages, and Programming (Vol. 198). Glasgow, Scotland:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2021.124'
chicago: Chatterjee, Krishnendu, Monika H Henzinger, Sagar Sudhir Kale, and Alexander
Svozil. “Faster Algorithms for Bounded Liveness in Graphs and Game Graphs.” In
48th International Colloquium on Automata, Languages, and Programming,
Vol. 198. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.ICALP.2021.124.
ieee: K. Chatterjee, M. H. Henzinger, S. S. Kale, and A. Svozil, “Faster algorithms
for bounded liveness in graphs and game graphs,” in 48th International Colloquium
on Automata, Languages, and Programming, Glasgow, Scotland, 2021, vol. 198.
ista: 'Chatterjee K, Henzinger MH, Kale SS, Svozil A. 2021. Faster algorithms for
bounded liveness in graphs and game graphs. 48th International Colloquium on Automata,
Languages, and Programming. ICALP: International Colloquium on Automata, Languages,
and Programming, LIPIcs, vol. 198, 124.'
mla: Chatterjee, Krishnendu, et al. “Faster Algorithms for Bounded Liveness in Graphs
and Game Graphs.” 48th International Colloquium on Automata, Languages, and
Programming, vol. 198, 124, Schloss Dagstuhl - Leibniz Zentrum für Informatik,
2021, doi:10.4230/LIPIcs.ICALP.2021.124.
short: K. Chatterjee, M.H. Henzinger, S.S. Kale, A. Svozil, in:, 48th International
Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz
Zentrum für Informatik, 2021.
conference:
end_date: 2021-07-16
location: Glasgow, Scotland
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2021-07-12
date_created: 2021-09-27T14:33:15Z
date_published: 2021-07-02T00:00:00Z
date_updated: 2022-08-12T10:55:02Z
day: '02'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.ICALP.2021.124
ec_funded: 1
file:
- access_level: open_access
checksum: 5a3fed8dbba8c088cbeac1e24cc10bc5
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T08:49:26Z
date_updated: 2021-10-01T08:49:26Z
file_id: '10062'
file_name: 2021_LIPIcs_Chatterjee.pdf
file_size: 854576
relation: main_file
success: 1
file_date_updated: 2021-10-01T08:49:26Z
has_accepted_license: '1'
intvolume: ' 198'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 48th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- 978-3-95977-195-5
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Faster algorithms for bounded liveness in graphs and game graphs
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: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 198
year: '2021'
...
---
_id: '10075'
abstract:
- lang: eng
text: We study the expressiveness and succinctness of good-for-games pushdown automata
(GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can
be resolved based on the run constructed so far, but independently of the remainder
of the input word. We prove that GFG-PDA recognise more languages than deterministic
PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal
to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct
than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We
also study GFGness in visibly pushdown automata (VPA), which enjoy better closure
properties than PDA, and for which we show GFGness to be ExpTime-complete. GFG-VPA
can be exponentially more succinct than deterministic VPA, while VPA can be exponentially
more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we
study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has
a positional resolver, a function that resolves nondeterminism and that is only
dependant on the current configuration. Pushdown transducers are sufficient to
implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state
resolvers are determinisable.
acknowledgement: 'Ismaël Jecker: Funded by the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie grant agreement No 754411.
Karoliina Lehtinen: Funded by the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No 892704.'
alternative_title:
- LIPIcs
article_number: '53'
article_processing_charge: No
author:
- first_name: Shibashis
full_name: Guha, Shibashis
last_name: Guha
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Karoliina
full_name: Lehtinen, Karoliina
last_name: Lehtinen
- first_name: Martin
full_name: Zimmermann, Martin
last_name: Zimmermann
citation:
ama: 'Guha S, Jecker IR, Lehtinen K, Zimmermann M. A bit of nondeterminism makes
pushdown automata expressive and succinct. In: 46th International Symposium
on Mathematical Foundations of Computer Science. Vol 202. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.MFCS.2021.53'
apa: 'Guha, S., Jecker, I. R., Lehtinen, K., & Zimmermann, M. (2021). A bit
of nondeterminism makes pushdown automata expressive and succinct. In 46th
International Symposium on Mathematical Foundations of Computer Science (Vol.
202). Tallinn, Estonia: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2021.53'
chicago: Guha, Shibashis, Ismael R Jecker, Karoliina Lehtinen, and Martin Zimmermann.
“A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct.” In
46th International Symposium on Mathematical Foundations of Computer Science,
Vol. 202. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.MFCS.2021.53.
ieee: S. Guha, I. R. Jecker, K. Lehtinen, and M. Zimmermann, “A bit of nondeterminism
makes pushdown automata expressive and succinct,” in 46th International Symposium
on Mathematical Foundations of Computer Science, Tallinn, Estonia, 2021, vol.
202.
ista: 'Guha S, Jecker IR, Lehtinen K, Zimmermann M. 2021. A bit of nondeterminism
makes pushdown automata expressive and succinct. 46th International Symposium
on Mathematical Foundations of Computer Science. MFCS: Mathematical Foundations
of Computer Science, LIPIcs, vol. 202, 53.'
mla: Guha, Shibashis, et al. “A Bit of Nondeterminism Makes Pushdown Automata Expressive
and Succinct.” 46th International Symposium on Mathematical Foundations of
Computer Science, vol. 202, 53, Schloss Dagstuhl - Leibniz Zentrum für Informatik,
2021, doi:10.4230/LIPIcs.MFCS.2021.53.
short: S. Guha, I.R. Jecker, K. Lehtinen, M. Zimmermann, in:, 46th International
Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl -
Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-27
location: Tallinn, Estonia
name: 'MFCS: Mathematical Foundations of Computer Science'
start_date: 2021-08-23
date_created: 2021-10-03T22:01:23Z
date_published: 2021-08-18T00:00:00Z
date_updated: 2022-05-13T08:21:56Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2021.53
ec_funded: 1
external_id:
arxiv:
- '2105.02611'
file:
- access_level: open_access
checksum: f4d407d43a97330c3fb11e6a7a6fbfb2
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-06T12:44:05Z
date_updated: 2021-10-06T12:44:05Z
file_id: '10097'
file_name: 2021_LIPIcs_Guha.pdf
file_size: 825567
relation: main_file
success: 1
file_date_updated: 2021-10-06T12:44:05Z
has_accepted_license: '1'
intvolume: ' 202'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 46th International Symposium on Mathematical Foundations of Computer
Science
publication_identifier:
isbn:
- 978-3-9597-7201-3
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A bit of nondeterminism makes pushdown automata expressive and succinct
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 202
year: '2021'
...
---
_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'
...
---
_id: '10629'
abstract:
- lang: eng
text: "Product graphs arise naturally in formal verification and program analysis.
For example, the analysis of two concurrent threads requires the product of two
component control-flow graphs, and for language inclusion of deterministic automata
the product of two automata is constructed. In many cases, the component graphs
have constant treewidth, e.g., when the input contains control-flow graphs of
programs. We consider the algorithmic analysis of products of two constant-treewidth
graphs with respect to three classic specification languages, namely, (a) algebraic
properties, (b) mean-payoff properties, and (c) initial credit for energy properties.\r\nOur
main contributions are as follows. Consider a graph G that is the product of two
constant-treewidth graphs of size n each. First, given an idempotent semiring,
we present an algorithm that computes the semiring transitive closure of G in
time Õ(n⁴). Since the output has size Θ(n⁴), our algorithm is optimal (up to
polylog factors). Second, given a mean-payoff objective, we present an O(n³)-time
algorithm for deciding whether the value of a starting state is non-negative,
improving the previously known O(n⁴) bound. Third, given an initial credit for
energy objective, we present an O(n⁵)-time algorithm for computing the minimum
initial credit for all nodes of G, improving the previously known O(n⁸) bound.
At the heart of our approach lies an algorithm for the efficient construction
of strongly-balanced tree decompositions of constant-treewidth graphs. Given a
constant-treewidth graph G' of n nodes and a positive integer λ, our algorithm
constructs a binary tree decomposition of G' of width O(λ) with the property that
the size of each subtree decreases geometrically with rate (1/2 + 2^{-λ})."
alternative_title:
- LIPIcs
article_number: '42'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Andreas
full_name: Pavlogiannis, Andreas
id: 49704004-F248-11E8-B48F-1D18A9856A87
last_name: Pavlogiannis
orcid: 0000-0002-8943-0722
citation:
ama: 'Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Quantitative verification on
product graphs of small treewidth. 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.2021.42'
apa: 'Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2021). Quantitative
verification on product graphs of small treewidth. 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.2021.42'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis.
“Quantitative Verification on Product Graphs of Small Treewidth.” 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.2021.42.
ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Quantitative verification
on product graphs of small treewidth,” in 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, Virtual, 2021, vol.
213.
ista: 'Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2021. Quantitative verification
on product graphs of small treewidth. 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, 42.'
mla: Chatterjee, Krishnendu, et al. “Quantitative Verification on Product Graphs
of Small Treewidth.” 41st IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, vol. 213, 42, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.FSTTCS.2021.42.
short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, 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: 2022-01-16T23:01:28Z
date_published: 2021-11-29T00:00:00Z
date_updated: 2022-01-17T10:39:40Z
day: '29'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2021.42
file:
- access_level: open_access
checksum: 71141acdeffa9056f24d6dbef952d254
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-17T10:36:08Z
date_updated: 2022-01-17T10:36:08Z
file_id: '10633'
file_name: 2021_LIPIcs_Chatterjee.pdf
file_size: 891566
relation: main_file
success: 1
file_date_updated: 2022-01-17T10:36:08Z
has_accepted_license: '1'
intvolume: ' 213'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
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: Quantitative verification on product graphs of small treewidth
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'
...
---
_id: '10694'
abstract:
- lang: eng
text: 'In a two-player zero-sum graph game the players move a token throughout a
graph to produce an infinite path, which determines the winner or payoff of the
game. Traditionally, the players alternate turns in moving the token. In bidding
games, however, the players have budgets, and in each turn, we hold an “auction”
(bidding) to determine which player moves the token: both players simultaneously
submit bids and the higher bidder moves the token. The bidding mechanisms differ
in their payment schemes. Bidding games were largely studied with variants of
first-price bidding in which only the higher bidder pays his bid. We focus on
all-pay bidding, where both players pay their bids. Finite-duration all-pay bidding
games were studied and shown to be technically more challenging than their first-price
counterparts. We study for the first time, infinite-duration all-pay bidding games.
Our most interesting results are for mean-payoff objectives: we portray a complete
picture for games played on strongly-connected graphs. We study both pure (deterministic)
and mixed (probabilistic) strategies and completely characterize the optimal and
almost-sure (with probability 1) payoffs the players can respectively guarantee.
We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical
properties of their first-price counterparts; namely, an equivalence with random-turn
games in which in each turn, the player who moves is selected according to a (biased)
coin toss. The equivalences for all-pay bidding are more intricate and unexpected
than for first-price bidding.'
acknowledgement: This research was supported in part by the Austrian Science Fund
(FWF) under grant Z211-N23 (Wittgenstein Award), ERC CoG 863818 (FoRM-SMArt), and
by the European Union's Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie Grant Agreement No. 665385.
article_processing_charge: No
author:
- first_name: Guy
full_name: Avni, Guy
id: 463C8BC2-F248-11E8-B48F-1D18A9856A87
last_name: Avni
orcid: 0000-0001-5588-8287
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Dorde
full_name: Zikelic, Dorde
id: 294AA7A6-F248-11E8-B48F-1D18A9856A87
last_name: Zikelic
citation:
ama: 'Avni G, Jecker IR, Zikelic D. Infinite-duration all-pay bidding games. In:
Marx D, ed. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms.
Society for Industrial and Applied Mathematics; 2021:617-636. doi:10.1137/1.9781611976465.38'
apa: 'Avni, G., Jecker, I. R., & Zikelic, D. (2021). Infinite-duration all-pay
bidding games. In D. Marx (Ed.), Proceedings of the 2021 ACM-SIAM Symposium
on Discrete Algorithms (pp. 617–636). Virtual: Society for Industrial and
Applied Mathematics. https://doi.org/10.1137/1.9781611976465.38'
chicago: Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Infinite-Duration All-Pay
Bidding Games.” In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms,
edited by Dániel Marx, 617–36. Society for Industrial and Applied Mathematics,
2021. https://doi.org/10.1137/1.9781611976465.38.
ieee: G. Avni, I. R. Jecker, and D. Zikelic, “Infinite-duration all-pay bidding
games,” in Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms,
Virtual, 2021, pp. 617–636.
ista: 'Avni G, Jecker IR, Zikelic D. 2021. Infinite-duration all-pay bidding games.
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium
on Discrete Algorithms, 617–636.'
mla: Avni, Guy, et al. “Infinite-Duration All-Pay Bidding Games.” Proceedings
of the 2021 ACM-SIAM Symposium on Discrete Algorithms, edited by Dániel Marx,
Society for Industrial and Applied Mathematics, 2021, pp. 617–36, doi:10.1137/1.9781611976465.38.
short: G. Avni, I.R. Jecker, D. Zikelic, in:, D. Marx (Ed.), Proceedings of the
2021 ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied
Mathematics, 2021, pp. 617–636.
conference:
end_date: 2021-01-13
location: Virtual
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2021-01-10
date_created: 2022-01-27T12:11:23Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2022-01-27T12:58:43Z
day: '01'
department:
- _id: GradSch
- _id: KrCh
doi: 10.1137/1.9781611976465.38
ec_funded: 1
editor:
- first_name: Dániel
full_name: Marx, Dániel
last_name: Marx
external_id:
arxiv:
- '2005.06636'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2005.06636
month: '01'
oa: 1
oa_version: Preprint
page: 617-636
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms
publication_identifier:
isbn:
- 978-1-61197-646-5
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Infinite-duration all-pay bidding games
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10847'
abstract:
- lang: eng
text: 'We study the two-player zero-sum extension of the partially observable stochastic
shortest-path problem where one agent has only partial information about the environment.
We formulate this problem as a partially observable stochastic game (POSG): given
a set of target states and negative rewards for each transition, the player with
imperfect information maximizes the expected undiscounted total reward until a
target state is reached. The second player with the perfect information aims for
the opposite. We base our formalism on POSGs with one-sided observability (OS-POSGs)
and give the following contributions: (1) we introduce a novel heuristic search
value iteration algorithm that iteratively solves depth-limited variants of the
game, (2) we derive the bound on the depth guaranteeing an arbitrary precision,
(3) we propose a novel upper-bound estimation that allows early terminations,
and (4) we experimentally evaluate the algorithm on a pursuit-evasion game.'
acknowledgement: "This research was supported by the Czech Science Foundation (no.
19-24384Y), by the OP VVV MEYS funded project CZ.02.1.01/0.0/0.0/16 019/0000765
“Research Center for Informatics”, by the ERC CoG 863818 (ForM-SMArt), and by the
Combat Capabilities Development Command Army Research Laboratory and was accomplished
under Cooperative\r\nAgreement Number W911NF-13-2-0045 (ARL Cyber Security CRA).
The views and conclusions contained in this document are those of the authors and
should not be interpreted as\r\nrepresenting the official policies, either expressed
or implied, of the Combat Capabilities Development Command Army Research Laboratory
or the U.S. Government. The U.S. Government is authorized to reproduce and distribute
reprints for Government purposes not withstanding any copyright notation here on. "
article_processing_charge: No
author:
- first_name: Petr
full_name: Tomášek, Petr
last_name: Tomášek
- first_name: Karel
full_name: Horák, Karel
last_name: Horák
- first_name: Aditya
full_name: Aradhye, Aditya
last_name: Aradhye
- first_name: Branislav
full_name: Bošanský, Branislav
last_name: Bošanský
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
citation:
ama: 'Tomášek P, Horák K, Aradhye A, Bošanský B, Chatterjee K. Solving partially
observable stochastic shortest-path games. In: 30th International Joint Conference
on Artificial Intelligence. International Joint Conferences on Artificial
Intelligence; 2021:4182-4189. doi:10.24963/ijcai.2021/575'
apa: 'Tomášek, P., Horák, K., Aradhye, A., Bošanský, B., & Chatterjee, K. (2021).
Solving partially observable stochastic shortest-path games. In 30th International
Joint Conference on Artificial Intelligence (pp. 4182–4189). Virtual, Online:
International Joint Conferences on Artificial Intelligence. https://doi.org/10.24963/ijcai.2021/575'
chicago: Tomášek, Petr, Karel Horák, Aditya Aradhye, Branislav Bošanský, and Krishnendu
Chatterjee. “Solving Partially Observable Stochastic Shortest-Path Games.” In
30th International Joint Conference on Artificial Intelligence, 4182–89.
International Joint Conferences on Artificial Intelligence, 2021. https://doi.org/10.24963/ijcai.2021/575.
ieee: P. Tomášek, K. Horák, A. Aradhye, B. Bošanský, and K. Chatterjee, “Solving
partially observable stochastic shortest-path games,” in 30th International
Joint Conference on Artificial Intelligence, Virtual, Online, 2021, pp. 4182–4189.
ista: 'Tomášek P, Horák K, Aradhye A, Bošanský B, Chatterjee K. 2021. Solving partially
observable stochastic shortest-path games. 30th International Joint Conference
on Artificial Intelligence. IJCAI: International Joint Conferences on Artificial
Intelligence Organization, 4182–4189.'
mla: Tomášek, Petr, et al. “Solving Partially Observable Stochastic Shortest-Path
Games.” 30th International Joint Conference on Artificial Intelligence,
International Joint Conferences on Artificial Intelligence, 2021, pp. 4182–89,
doi:10.24963/ijcai.2021/575.
short: P. Tomášek, K. Horák, A. Aradhye, B. Bošanský, K. Chatterjee, in:, 30th International
Joint Conference on Artificial Intelligence, International Joint Conferences on
Artificial Intelligence, 2021, pp. 4182–4189.
conference:
end_date: 2021-08-27
location: Virtual, Online
name: 'IJCAI: International Joint Conferences on Artificial Intelligence Organization'
start_date: 2021-08-19
date_created: 2022-03-13T23:01:47Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2022-08-05T09:05:06Z
day: '01'
department:
- _id: KrCh
doi: 10.24963/ijcai.2021/575
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.24963/ijcai.2021/575
month: '09'
oa: 1
oa_version: Published Version
page: 4182-4189
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 30th International Joint Conference on Artificial Intelligence
publication_identifier:
isbn:
- '9780999241196'
issn:
- 1045-0823
publication_status: published
publisher: International Joint Conferences on Artificial Intelligence
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solving partially observable stochastic shortest-path games
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9296'
abstract:
- lang: eng
text: ' matching is compatible to two or more labeled point sets of size n with
labels {1,…,n} if its straight-line drawing on each of these point sets is
crossing-free. We study the maximum number of edges in a matching compatible to
two or more labeled point sets in general position in the plane. We show that
for any two labeled convex sets of n points there exists a compatible matching
with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct
compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use
probabilistic arguments to show that for any ℓ given sets of n points there
exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges.
Finally, we show that Θ(logn) copies of any set of n points are necessary and
sufficient for the existence of a labeling such that any compatible matching consists
only of a single edge.'
acknowledgement: 'A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411.
Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant
no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported
by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by
ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23
(RiSE).'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Daniel
full_name: Perz, Daniel
last_name: Perz
- first_name: Alexander
full_name: Pilz, Alexander
last_name: Pilz
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings.
In: 15th International Conference on Algorithms and Computation. Vol 12635.
Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18'
apa: 'Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D.,
Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International
Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon,
Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18'
chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada,
Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible
Matchings.” In 15th International Conference on Algorithms and Computation,
12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.
ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International
Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635,
pp. 221–233.
ista: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec
J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference
on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol.
12635, 221–233.'
mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International
Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021,
pp. 221–33, doi:10.1007/978-3-030-68211-8_18.
short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz,
J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and
Computation, Springer Nature, 2021, pp. 221–233.
conference:
end_date: 2021-03-02
location: Yangon, Myanmar
name: 'WALCOM: Algorithms and Computation'
start_date: 2021-02-28
date_created: 2021-03-28T22:01:41Z
date_published: 2021-02-16T00:00:00Z
date_updated: 2023-02-21T16:33:44Z
day: '16'
department:
- _id: UlWa
- _id: HeEd
- _id: KrCh
doi: 10.1007/978-3-030-68211-8_18
ec_funded: 1
external_id:
arxiv:
- '2101.03928'
intvolume: ' 12635'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.03928
month: '02'
oa: 1
oa_version: Preprint
page: 221-233
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: The Wittgenstein Prize
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
publication: 15th International Conference on Algorithms and Computation
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030682101'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11938'
relation: later_version
status: public
scopus_import: '1'
status: public
title: On compatible matchings
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 12635
year: '2021'
...
---
_id: '9403'
abstract:
- lang: eng
text: Optimal decision making requires individuals to know their available options
and to anticipate correctly what consequences these options have. In many social
interactions, however, we refrain from gathering all relevant information, even
if this information would help us make better decisions and is costless to obtain.
This chapter examines several examples of “deliberate ignorance.” Two simple models
are proposed to illustrate how ignorance can evolve among self-interested and
payoff - maximizing individuals, and open problems are highlighted that lie ahead
for future research to explore.
article_processing_charge: No
author:
- first_name: Laura
full_name: Schmid, Laura
id: 38B437DE-F248-11E8-B48F-1D18A9856A87
last_name: Schmid
orcid: 0000-0002-6978-7329
- first_name: Christian
full_name: Hilbe, Christian
last_name: Hilbe
citation:
ama: 'Schmid L, Hilbe C. The evolution of strategic ignorance in strategic interaction.
In: Hertwig R, Engel C, eds. Deliberate Ignorance: Choosing Not To Know.
Vol 29. Strüngmann Forum Reports. MIT Press; 2021:139-152.'
apa: 'Schmid, L., & Hilbe, C. (2021). The evolution of strategic ignorance in
strategic interaction. In R. Hertwig & C. Engel (Eds.), Deliberate Ignorance:
Choosing Not To Know (Vol. 29, pp. 139–152). MIT Press.'
chicago: 'Schmid, Laura, and Christian Hilbe. “The Evolution of Strategic Ignorance
in Strategic Interaction.” In Deliberate Ignorance: Choosing Not To Know,
edited by Ralph Hertwig and Christoph Engel, 29:139–52. Strüngmann Forum Reports.
MIT Press, 2021.'
ieee: 'L. Schmid and C. Hilbe, “The evolution of strategic ignorance in strategic
interaction,” in Deliberate Ignorance: Choosing Not To Know, vol. 29, R.
Hertwig and C. Engel, Eds. MIT Press, 2021, pp. 139–152.'
ista: 'Schmid L, Hilbe C. 2021.The evolution of strategic ignorance in strategic
interaction. In: Deliberate Ignorance: Choosing Not To Know. vol. 29, 139–152.'
mla: 'Schmid, Laura, and Christian Hilbe. “The Evolution of Strategic Ignorance
in Strategic Interaction.” Deliberate Ignorance: Choosing Not To Know,
edited by Ralph Hertwig and Christoph Engel, vol. 29, MIT Press, 2021, pp. 139–52.'
short: 'L. Schmid, C. Hilbe, in:, R. Hertwig, C. Engel (Eds.), Deliberate Ignorance:
Choosing Not To Know, MIT Press, 2021, pp. 139–152.'
date_created: 2021-05-19T12:25:42Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-02-23T13:57:04Z
day: '01'
department:
- _id: GradSch
- _id: KrCh
editor:
- first_name: Ralph
full_name: Hertwig, Ralph
last_name: Hertwig
- first_name: Christoph
full_name: Engel, Christoph
last_name: Engel
intvolume: ' 29'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://esforum.de/publications/PDFs/sfr29/SFR29_09_Hilbe%20and%20Schmid.pdf
month: '03'
oa: 1
oa_version: Published Version
page: 139-152
publication: 'Deliberate Ignorance: Choosing Not To Know'
publication_identifier:
isbn:
- 978-0-262-04559-9
publisher: MIT Press
quality_controlled: '1'
series_title: Strüngmann Forum Reports
status: public
title: The evolution of strategic ignorance in strategic interaction
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2021'
...