---
_id: '552'
abstract:
- lang: eng
text: 'Graph games provide the foundation for modeling and synthesis of reactive
processes. Such games are played over graphs where the vertices are controlled
by two adversarial players. We consider graph games where the objective of the
first player is the conjunction of a qualitative objective (specified as a parity
condition) and a quantitative objective (specified as a meanpayoff condition).
There are two variants of the problem, namely, the threshold problem where the
quantitative goal is to ensure that the mean-payoff value is above a threshold,
and the value problem where the quantitative goal is to ensure the optimal mean-payoff
value; in both cases ensuring the qualitative parity objective. The previous best-known
algorithms for game graphs with n vertices, m edges, parity objectives with d
priorities, and maximal absolute reward value W for mean-payoff objectives, are
as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for
the value problem. Our main contributions are faster algorithms, and the running
times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem,
and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives
with two priorities, our algorithms match the best-known bounds of the algorithms
for mean-payoff games (without conjunction with parity objectives). Our results
are relevant in synthesis of reactive systems with both functional requirement
(given as a qualitative objective) and performance requirement (given as a quantitative
objective).'
alternative_title:
- LIPIcs
article_number: '39'
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: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Henzinger MH, Svozil A. Faster algorithms for mean-payoff parity
games. In: Leibniz International Proceedings in Informatics. Vol 83. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.MFCS.2017.39'
apa: 'Chatterjee, K., Henzinger, M. H., & Svozil, A. (2017). Faster algorithms
for mean-payoff parity games. In Leibniz International Proceedings in Informatics
(Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.MFCS.2017.39'
chicago: Chatterjee, Krishnendu, Monika H Henzinger, and Alexander Svozil. “Faster
Algorithms for Mean-Payoff Parity Games.” In Leibniz International Proceedings
in Informatics, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.MFCS.2017.39.
ieee: K. Chatterjee, M. H. Henzinger, and A. Svozil, “Faster algorithms for mean-payoff
parity games,” in Leibniz International Proceedings in Informatics, Aalborg,
Denmark, 2017, vol. 83.
ista: 'Chatterjee K, Henzinger MH, Svozil A. 2017. Faster algorithms for mean-payoff
parity games. Leibniz International Proceedings in Informatics. MFCS: Mathematical
Foundations of Computer Science (SG), LIPIcs, vol. 83, 39.'
mla: Chatterjee, Krishnendu, et al. “Faster Algorithms for Mean-Payoff Parity Games.”
Leibniz International Proceedings in Informatics, vol. 83, 39, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.MFCS.2017.39.
short: K. Chatterjee, M.H. Henzinger, A. Svozil, in:, Leibniz International Proceedings
in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
conference:
end_date: 2017-08-25
location: Aalborg, Denmark
name: 'MFCS: Mathematical Foundations of Computer Science (SG)'
start_date: 2017-08-21
date_created: 2018-12-11T11:47:08Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-02-14T10:06:46Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2017.39
ec_funded: 1
file:
- access_level: open_access
checksum: c67f4866ddbfd555afef1f63ae9a8fc7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:57Z
date_updated: 2020-07-14T12:47:00Z
file_id: '5248'
file_name: IST-2018-923-v1+1_LIPIcs-MFCS-2017-39.pdf
file_size: 610339
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 83'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- 978-395977046-0
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7262'
pubrep_id: '923'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Faster algorithms for mean-payoff parity games
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2017'
...
---
_id: '553'
abstract:
- lang: eng
text: 'We consider two player, zero-sum, finite-state concurrent reachability games,
played for an infinite number of rounds, where in every round, each player simultaneously
and independently of the other players chooses an action, whereafter the successor
state is determined by a probability distribution given by the current state and
the chosen actions. Player 1 wins iff a designated goal state is eventually visited.
We are interested in the complexity of stationary strategies measured by their
patience, which is defined as the inverse of the smallest non-zero probability
employed. Our main results are as follows: We show that: (i) the optimal bound
on the patience of optimal and -optimal strategies, for both players is doubly
exponential; and (ii) even in games with a single non-absorbing state exponential
(in the number of actions) patience is necessary. '
alternative_title:
- LIPIcs
article_number: '55'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Kristofer
full_name: Hansen, Kristofer
last_name: Hansen
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
citation:
ama: 'Chatterjee K, Hansen K, Ibsen-Jensen R. Strategy complexity of concurrent
safety games. In: Leibniz International Proceedings in Informatics. Vol
83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.MFCS.2017.55'
apa: 'Chatterjee, K., Hansen, K., & Ibsen-Jensen, R. (2017). Strategy complexity
of concurrent safety games. In Leibniz International Proceedings in Informatics
(Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.MFCS.2017.55'
chicago: Chatterjee, Krishnendu, Kristofer Hansen, and Rasmus Ibsen-Jensen. “Strategy
Complexity of Concurrent Safety Games.” In Leibniz International Proceedings
in Informatics, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.MFCS.2017.55.
ieee: K. Chatterjee, K. Hansen, and R. Ibsen-Jensen, “Strategy complexity of concurrent
safety games,” in Leibniz International Proceedings in Informatics, Aalborg,
Denmark, 2017, vol. 83.
ista: 'Chatterjee K, Hansen K, Ibsen-Jensen R. 2017. Strategy complexity of concurrent
safety games. Leibniz International Proceedings in Informatics. MFCS: Mathematical
Foundations of Computer Science (SG), LIPIcs, vol. 83, 55.'
mla: Chatterjee, Krishnendu, et al. “Strategy Complexity of Concurrent Safety Games.”
Leibniz International Proceedings in Informatics, vol. 83, 55, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.MFCS.2017.55.
short: K. Chatterjee, K. Hansen, R. Ibsen-Jensen, in:, Leibniz International Proceedings
in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
conference:
end_date: 2017-08-25
location: Aalborg, Denmark
name: 'MFCS: Mathematical Foundations of Computer Science (SG)'
start_date: 2017-08-21
date_created: 2018-12-11T11:47:08Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:02:35Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2017.55
file:
- access_level: open_access
checksum: 7101facb56ade363205c695d72dbd173
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:29Z
date_updated: 2020-07-14T12:47:00Z
file_id: '4753'
file_name: IST-2018-922-v1+1_LIPIcs-MFCS-2017-55.pdf
file_size: 549967
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 83'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.02434
month: '11'
oa: 1
oa_version: Published Version
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- 978-395977046-0
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7261'
pubrep_id: '922'
quality_controlled: '1'
scopus_import: 1
status: public
title: Strategy complexity of concurrent safety games
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2017'
...
---
_id: '560'
abstract:
- lang: eng
text: In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500
(doi:10.4310/CMS.2016.v14. n6.a1)), it has been established that, for every arbitrarily
slow convergence speed and every natural number d ? {4, 5, . . .}, there exist
d-dimensional stochastic differential equations with infinitely often differentiable
and globally bounded coefficients such that no approximation method based on finitely
many observations of the driving Brownian motion can converge in absolute mean
to the solution faster than the given speed of convergence. In this paper, we
strengthen the above result by proving that this slow convergence phenomenon also
arises in two (d = 2) and three (d = 3) space dimensions.
article_number: '0104'
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Arnulf
full_name: Jentzen, Arnulf
last_name: Jentzen
- first_name: Diyora
full_name: Salimova, Diyora
last_name: Salimova
citation:
ama: 'Gerencser M, Jentzen A, Salimova D. On stochastic differential equations with
arbitrarily slow convergence rates for strong approximation in two space dimensions.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences. 2017;473(2207). doi:10.1098/rspa.2017.0104'
apa: 'Gerencser, M., Jentzen, A., & Salimova, D. (2017). On stochastic differential
equations with arbitrarily slow convergence rates for strong approximation in
two space dimensions. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. Royal Society of London. https://doi.org/10.1098/rspa.2017.0104'
chicago: 'Gerencser, Mate, Arnulf Jentzen, and Diyora Salimova. “On Stochastic Differential
Equations with Arbitrarily Slow Convergence Rates for Strong Approximation in
Two Space Dimensions.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. Royal Society of London, 2017. https://doi.org/10.1098/rspa.2017.0104.'
ieee: 'M. Gerencser, A. Jentzen, and D. Salimova, “On stochastic differential equations
with arbitrarily slow convergence rates for strong approximation in two space
dimensions,” Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences, vol. 473, no. 2207. Royal Society of London, 2017.'
ista: 'Gerencser M, Jentzen A, Salimova D. 2017. On stochastic differential equations
with arbitrarily slow convergence rates for strong approximation in two space
dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences. 473(2207), 0104.'
mla: 'Gerencser, Mate, et al. “On Stochastic Differential Equations with Arbitrarily
Slow Convergence Rates for Strong Approximation in Two Space Dimensions.” Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.
473, no. 2207, 0104, Royal Society of London, 2017, doi:10.1098/rspa.2017.0104.'
short: 'M. Gerencser, A. Jentzen, D. Salimova, Proceedings of the Royal Society
A: Mathematical, Physical and Engineering Sciences 473 (2017).'
date_created: 2018-12-11T11:47:11Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:03:04Z
day: '01'
department:
- _id: JaMa
doi: 10.1098/rspa.2017.0104
ec_funded: 1
intvolume: ' 473'
issue: '2207'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.03229
month: '11'
oa: 1
oa_version: Submitted Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences'
publication_identifier:
issn:
- '13645021'
publication_status: published
publisher: Royal Society of London
publist_id: '7256'
quality_controlled: '1'
scopus_import: 1
status: public
title: On stochastic differential equations with arbitrarily slow convergence rates
for strong approximation in two space dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 473
year: '2017'
...
---
_id: '567'
abstract:
- lang: eng
text: "This book is a concise and self-contained introduction of recent techniques
to prove local spectral universality for large random matrices. Random matrix
theory is a fast expanding research area, and this book mainly focuses on the
methods that the authors participated in developing over the past few years. Many
other interesting topics are not included, and neither are several new developments
within the framework of these methods. The authors have chosen instead to present
key concepts that they believe are the core of these methods and should be relevant
for future applications. They keep technicalities to a minimum to make the book
accessible to graduate students. With this in mind, they include in this book
the basic notions and tools for high-dimensional analysis, such as large deviation,
entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"
alternative_title:
- Courant Lecture Notes
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28.
American Mathematical Society; 2017. doi:10.1090/cln/028
apa: Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory
(Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028
chicago: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix
Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017.
https://doi.org/10.1090/cln/028.
ieee: L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory,
vol. 28. American Mathematical Society, 2017.
ista: Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 226p.
mla: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory.
Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.
short: L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 2017.
date_created: 2018-12-11T11:47:13Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2022-05-24T06:57:28Z
day: '01'
department:
- _id: LaEr
doi: 10.1090/cln/028
ec_funded: 1
intvolume: ' 28'
language:
- iso: eng
month: '01'
oa_version: None
page: '226'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
eisbn:
- 978-1-4704-4194-4
isbn:
- 9-781-4704-3648-3
publication_status: published
publisher: American Mathematical Society
publist_id: '7247'
quality_controlled: '1'
series_title: Courant Lecture Notes
status: public
title: A Dynamical Approach to Random Matrix Theory
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...
---
_id: '568'
abstract:
- lang: eng
text: 'We study robust properties of zero sets of continuous maps f: X → ℝn. Formally,
we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets
of all continuous maps g closer to f than r in the max-norm. All of these sets
are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined
by A and an element of a certain cohomotopy group which (by a recent result) is
computable whenever the dimension of X is at most 2n - 3. By considering all r
> 0 simultaneously, the pointed cohomotopy groups form a persistence module-a
structure leading to persistence diagrams as in the case of persistent homology
or well groups. Eventually, we get a descriptor of persistent robust properties
of zero sets that has better descriptive power (Theorem A) and better computability
status (Theorem B) than the established well diagrams. Moreover, if we endow every
point of each zero set with gradients of the perturbation, the robust description
of the zero sets by elements of cohomotopy groups is in some sense the best possible
(Theorem C).'
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications.
2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16
apa: Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology,
Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16
chicago: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology,
Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.
ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy
and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.
ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and
Applications. 19(2), 313–342.
mla: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy
and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.
short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.
date_created: 2018-12-11T11:47:14Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:03:12Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4310/HHA.2017.v19.n2.a16
ec_funded: 1
intvolume: ' 19'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1507.04310
month: '01'
oa: 1
oa_version: Submitted Version
page: 313 - 342
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 2590DB08-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '701309'
name: Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes
(H2020)
publication: Homology, Homotopy and Applications
publication_identifier:
issn:
- '15320073'
publication_status: published
publisher: International Press
publist_id: '7246'
quality_controlled: '1'
scopus_import: 1
status: public
title: Persistence of zero sets
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2017'
...