---
_id: '497'
abstract:
- lang: eng
text: 'One central issue in the formal design and analysis of reactive systems is
the notion of refinement that asks whether all behaviors of the implementation
is allowed by the specification. The local interpretation of behavior leads to
the notion of simulation. Alternating transition systems (ATSs) provide a general
model for composite reactive systems, and the simulation relation for ATSs is
known as alternating simulation. The simulation relation for fair transition systems
is called fair simulation. In this work our main contributions are as follows:
(1) We present an improved algorithm for fair simulation with Büchi fairness constraints;
our algorithm requires O(n 3·m) time as compared to the previous known O(n 6)-time
algorithm, where n is the number of states and m is the number of transitions.
(2) We present a game based algorithm for alternating simulation that requires
O(m2)-time as compared to the previous known O((n·m)2)-time algorithm, where n
is the number of states and m is the size of transition relation. (3) We present
an iterative algorithm for alternating simulation that matches the time complexity
of the game based algorithm, but is more space efficient than the game based algorithm.
© Krishnendu Chatterjee, Siddhesh Chaubal, and Pritish Kamath.'
alternative_title:
- LIPIcs
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Siddhesh
full_name: Chaubal, Siddhesh
last_name: Chaubal
- first_name: Pritish
full_name: Kamath, Pritish
last_name: Kamath
citation:
ama: 'Chatterjee K, Chaubal S, Kamath P. Faster algorithms for alternating refinement
relations. In: Vol 16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2012:167-182.
doi:10.4230/LIPIcs.CSL.2012.167'
apa: 'Chatterjee, K., Chaubal, S., & Kamath, P. (2012). Faster algorithms for
alternating refinement relations (Vol. 16, pp. 167–182). Presented at the EACSL:
European Association for Computer Science Logic, Fontainebleau, France: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CSL.2012.167'
chicago: Chatterjee, Krishnendu, Siddhesh Chaubal, and Pritish Kamath. “Faster Algorithms
for Alternating Refinement Relations,” 16:167–82. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2012. https://doi.org/10.4230/LIPIcs.CSL.2012.167.
ieee: 'K. Chatterjee, S. Chaubal, and P. Kamath, “Faster algorithms for alternating
refinement relations,” presented at the EACSL: European Association for Computer
Science Logic, Fontainebleau, France, 2012, vol. 16, pp. 167–182.'
ista: 'Chatterjee K, Chaubal S, Kamath P. 2012. Faster algorithms for alternating
refinement relations. EACSL: European Association for Computer Science Logic,
LIPIcs, vol. 16, 167–182.'
mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Alternating Refinement
Relations. Vol. 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012,
pp. 167–82, doi:10.4230/LIPIcs.CSL.2012.167.
short: K. Chatterjee, S. Chaubal, P. Kamath, in:, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2012, pp. 167–182.
conference:
end_date: 2012-09-06
location: Fontainebleau, France
name: 'EACSL: European Association for Computer Science Logic'
start_date: 2012-09-03
date_created: 2018-12-11T11:46:48Z
date_published: 2012-09-01T00:00:00Z
date_updated: 2023-02-23T12:23:32Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.CSL.2012.167
ec_funded: 1
file:
- access_level: open_access
checksum: f1b0dd99240800db2d7dbf9b5131fe5e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:50Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4712'
file_name: IST-2018-943-v1+1_2012_Chatterjee_Faster_Algorithms.pdf
file_size: 471236
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intvolume: ' 16'
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month: '09'
oa: 1
oa_version: Published Version
page: 167 - 182
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7323'
pubrep_id: '943'
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: 1
status: public
title: Faster algorithms for alternating refinement relations
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
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short: CC BY-NC-ND (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2012'
...
---
_id: '3165'
abstract:
- lang: eng
text: Computing the winning set for Büchi objectives in alternating games on graphs
is a central problem in computer aided verification with a large number of applications.
The long standing best known upper bound for solving the problem is Õ(n·m), where
n is the number of vertices and m is the number of edges in the graph. We are
the first to break the Õ(n·m) boundary by presenting a new technique that reduces
the running time to O(n 2). This bound also leads to O(n 2) time algorithms for
computing the set of almost-sure winning vertices for Büchi objectives (1) in
alternating games with probabilistic transitions (improving an earlier bound of
Õ(n·m)), (2) in concurrent graph games with constant actions (improving an earlier
bound of O(n 3)), and (3) in Markov decision processes (improving for m > n
4/3 an earlier bound of O(min(m 1.5, m·n 2/3)). We also show that the same technique
can be used to compute the maximal end-component decomposition of a graph in time
O(n 2), which is an improvement over earlier bounds for m > n 4/3. Finally,
we show how to maintain the winning set for Büchi objectives in alternating games
under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized
time per operation. This is the first dynamic algorithm for this problem.
acknowledgement: 'The research was supported by Austrian Science Fund (FWF) Grant
No P 23499-N23 on Modern Graph Algorithmic Techniques in Formal Verification, Vienna
Science and Technology Fund (WWTF) Grant ICT10-002, FWF NFN Grant No S11407-N23
(RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.'
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
citation:
ama: 'Chatterjee K, Henzinger MH. An O(n2) time algorithm for alternating Büchi
games. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.
SIAM; 2012:1386-1399. doi:10.1137/1.9781611973099.109'
apa: 'Chatterjee, K., & Henzinger, M. H. (2012). An O(n2) time algorithm for
alternating Büchi games. In Proceedings of the Annual ACM-SIAM Symposium on
Discrete Algorithms (pp. 1386–1399). Kyoto, Japan: SIAM. https://doi.org/10.1137/1.9781611973099.109'
chicago: Chatterjee, Krishnendu, and Monika H Henzinger. “An O(N2) Time Algorithm
for Alternating Büchi Games.” In Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, 1386–99. SIAM, 2012. https://doi.org/10.1137/1.9781611973099.109.
ieee: K. Chatterjee and M. H. Henzinger, “An O(n2) time algorithm for alternating
Büchi games,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms,
Kyoto, Japan, 2012, pp. 1386–1399.
ista: 'Chatterjee K, Henzinger MH. 2012. An O(n2) time algorithm for alternating
Büchi games. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.
SODA: Symposium on Discrete Algorithms, 1386–1399.'
mla: Chatterjee, Krishnendu, and Monika H. Henzinger. “An O(N2) Time Algorithm for
Alternating Büchi Games.” Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms, SIAM, 2012, pp. 1386–99, doi:10.1137/1.9781611973099.109.
short: K. Chatterjee, M.H. Henzinger, in:, Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, SIAM, 2012, pp. 1386–1399.
conference:
end_date: 2012-01-19
location: Kyoto, Japan
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2012-01-17
date_created: 2018-12-11T12:01:46Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2023-02-23T12:23:35Z
day: '01'
department:
- _id: KrCh
doi: 10.1137/1.9781611973099.109
ec_funded: 1
external_id:
arxiv:
- '1109.5018'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1109.5018
month: '01'
oa: 1
oa_version: None
page: 1386 - 1399
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_status: published
publisher: SIAM
publist_id: '3519'
pubrep_id: '15'
quality_controlled: '1'
related_material:
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relation: earlier_version
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status: public
title: An O(n2) time algorithm for alternating Büchi games
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '2956'
abstract:
- lang: eng
text: 'Two-player games on graphs are central in many problems in formal verification
and program analysis such as synthesis and verification of open systems. In this
work we consider solving recursive game graphs (or pushdown game graphs) that
can model the control flow of sequential programs with recursion. While pushdown
games have been studied before with qualitative objectives, such as reachability
and parity objectives, in this work we study for the first time such games with
the most well-studied quantitative objective, namely, mean payoff objectives.
In pushdown games two types of strategies are relevant: (1) global strategies,
that depend on the entire global history; and (2) modular strategies, that have
only local memory and thus do not depend on the context of invocation, but only
on the history of the current invocation of the module. Our main results are as
follows: (1) One-player pushdown games with mean-payoff objectives under global
strategies are decidable in polynomial time. (2) Two-player pushdown games with
mean-payoff objectives under global strategies are undecidable. (3) One-player
pushdown games with mean-payoff objectives under modular strategies are NP-hard.
(4) Two-player pushdown games with mean-payoff objectives under modular strategies
can be solved in NP (i.e., both one-player and two-player pushdown games with
mean-payoff objectives under modular strategies are NP-complete). We also establish
the optimal strategy complexity showing that global strategies for mean-payoff
objectives require infinite memory even in one-player pushdown games; and memoryless
modular strategies are sufficient in two-player pushdown games. Finally we also
show that all the problems have the same computational complexity if the stack
boundedness condition is added, where along with the mean-payoff objective the
player must also ensure that the stack height is bounded.'
acknowledgement: "The research was supported by Austrian Science Fund (FWF) Grant
No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph
Games), Microsoft faculty fellows award, the Israeli Centers of Research Excellence
(ICORE) program, (Center No. 4/11), the RICH Model Toolkit (ICT COST Action IC0901),
and was carried out in partial fulfillment of the requirements for the Ph.D. degree
of the second author.\r\nA Technical Report of this paper is available via internal
link."
article_number: '6280438'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Yaron
full_name: Velner, Yaron
last_name: Velner
citation:
ama: 'Chatterjee K, Velner Y. Mean payoff pushdown games. In: Proceedings of
the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. IEEE;
2012. doi:10.1109/LICS.2012.30'
apa: 'Chatterjee, K., & Velner, Y. (2012). Mean payoff pushdown games. In Proceedings
of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. Dubrovnik,
Croatia : IEEE. https://doi.org/10.1109/LICS.2012.30'
chicago: Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.”
In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer
Science. IEEE, 2012. https://doi.org/10.1109/LICS.2012.30.
ieee: K. Chatterjee and Y. Velner, “Mean payoff pushdown games,” in Proceedings
of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Dubrovnik,
Croatia , 2012.
ista: 'Chatterjee K, Velner Y. 2012. Mean payoff pushdown games. Proceedings of
the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic
in Computer Science, 6280438.'
mla: Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.” Proceedings
of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, 6280438,
IEEE, 2012, doi:10.1109/LICS.2012.30.
short: K. Chatterjee, Y. Velner, in:, Proceedings of the 2012 27th Annual ACM/IEEE
Symposium on Logic in Computer Science, IEEE, 2012.
conference:
end_date: 2012-06-28
location: 'Dubrovnik, Croatia '
name: 'LICS: Logic in Computer Science'
start_date: 2012-06-25
date_created: 2018-12-11T12:00:32Z
date_published: 2012-08-23T00:00:00Z
date_updated: 2023-02-23T12:23:30Z
day: '23'
department:
- _id: KrCh
doi: 10.1109/LICS.2012.30
ec_funded: 1
language:
- iso: eng
month: '08'
oa_version: None
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_status: published
publisher: IEEE
publist_id: '3770'
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: 1
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title: Mean payoff pushdown games
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '5377'
abstract:
- lang: eng
text: 'Two-player games on graphs are central in many problems in formal verification
and program analysis such as synthesis and verification of open systems. In this
work we consider solving recursive game graphs (or pushdown game graphs) that
can model the control flow of sequential programs with recursion. While pushdown
games have been studied before with qualitative objectives, such as reachability
and ω-regular objectives, in this work we study for the first time such games
with the most well-studied quantitative objective, namely, mean-payoff objectives.
In pushdown games two types of strategies are relevant: (1) global strategies,
that depend on the entire global history; and (2) modular strategies, that have
only local memory and thus do not depend on the context of invocation, but only
on the history of the current invocation of the module. Our main results are as
follows: (1) One-player pushdown games with mean-payoff objectives under global
strategies are decidable in polynomial time. (2) Two- player pushdown games with
mean-payoff objectives under global strategies are undecidable. (3) One-player
pushdown games with mean-payoff objectives under modular strategies are NP- hard.
(4) Two-player pushdown games with mean-payoff objectives under modular strategies
can be solved in NP (i.e., both one-player and two-player pushdown games with
mean-payoff objectives under modular strategies are NP-complete). We also establish
the optimal strategy complexity showing that global strategies for mean-payoff
objectives require infinite memory even in one-player pushdown games; and memoryless
modular strategies are sufficient in two- player pushdown games. Finally we also
show that all the problems have the same complexity if the stack boundedness condition
is added, where along with the mean-payoff objective the player must also ensure
that the stack height is bounded.'
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Yaron
full_name: Velner, Yaron
last_name: Velner
citation:
ama: Chatterjee K, Velner Y. Mean-Payoff Pushdown Games. IST Austria; 2012.
doi:10.15479/AT:IST-2012-0002
apa: Chatterjee, K., & Velner, Y. (2012). Mean-payoff pushdown games.
IST Austria. https://doi.org/10.15479/AT:IST-2012-0002
chicago: Chatterjee, Krishnendu, and Yaron Velner. Mean-Payoff Pushdown Games.
IST Austria, 2012. https://doi.org/10.15479/AT:IST-2012-0002.
ieee: K. Chatterjee and Y. Velner, Mean-payoff pushdown games. IST Austria,
2012.
ista: Chatterjee K, Velner Y. 2012. Mean-payoff pushdown games, IST Austria, 33p.
mla: Chatterjee, Krishnendu, and Yaron Velner. Mean-Payoff Pushdown Games.
IST Austria, 2012, doi:10.15479/AT:IST-2012-0002.
short: K. Chatterjee, Y. Velner, Mean-Payoff Pushdown Games, IST Austria, 2012.
date_created: 2018-12-12T11:38:59Z
date_published: 2012-07-02T00:00:00Z
date_updated: 2023-02-23T11:05:50Z
day: '02'
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year: '2012'
...
---
_id: '5378'
abstract:
- lang: eng
text: 'One central issue in the formal design and analysis of reactive systems is
the notion of refinement that asks whether all behaviors of the implementation
is allowed by the specification. The local interpretation of behavior leads to
the notion of simulation. Alternating transition systems (ATSs) provide a general
model for composite reactive systems, and the simulation relation for ATSs is
known as alternating simulation. The simulation relation for fair transition systems
is called fair simulation. In this work our main contributions are as follows:
(1) We present an improved algorithm for fair simulation with Büchi fairness constraints;
our algorithm requires O(n3 · m) time as compared to the previous known O(n6)-time
algorithm, where n is the number of states and m is the number of transitions.
(2) We present a game based algorithm for alternating simulation that requires
O(m2)-time as compared to the previous known O((n · m)2)-time algorithm, where
n is the number of states and m is the size of transition relation. (3) We present
an iterative algorithm for alternating simulation that matches the time complexity
of the game based algorithm, but is more space efficient than the game based algorithm.'
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Siddhesh
full_name: Chaubal, Siddhesh
last_name: Chaubal
- first_name: Pritish
full_name: Kamath, Pritish
last_name: Kamath
citation:
ama: Chatterjee K, Chaubal S, Kamath P. Faster Algorithms for Alternating Refinement
Relations. IST Austria; 2012. doi:10.15479/AT:IST-2012-0001
apa: Chatterjee, K., Chaubal, S., & Kamath, P. (2012). Faster algorithms
for alternating refinement relations. IST Austria. https://doi.org/10.15479/AT:IST-2012-0001
chicago: Chatterjee, Krishnendu, Siddhesh Chaubal, and Pritish Kamath. Faster
Algorithms for Alternating Refinement Relations. IST Austria, 2012. https://doi.org/10.15479/AT:IST-2012-0001.
ieee: K. Chatterjee, S. Chaubal, and P. Kamath, Faster algorithms for alternating
refinement relations. IST Austria, 2012.
ista: Chatterjee K, Chaubal S, Kamath P. 2012. Faster algorithms for alternating
refinement relations, IST Austria, 21p.
mla: Chatterjee, Krishnendu, et al. Faster Algorithms for Alternating Refinement
Relations. IST Austria, 2012, doi:10.15479/AT:IST-2012-0001.
short: K. Chatterjee, S. Chaubal, P. Kamath, Faster Algorithms for Alternating Refinement
Relations, IST Austria, 2012.
date_created: 2018-12-12T11:38:59Z
date_published: 2012-07-04T00:00:00Z
date_updated: 2023-02-23T12:21:38Z
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publication_status: published
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title: Faster algorithms for alternating refinement relations
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