---
_id: '5379'
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 ̃O(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 ̃O(n·m) boundary by presenting a new technique that reduces
the running time to O(n2). This bound also leads to O(n2) 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
O(n·m)), (2) in concurrent graph games with constant actions (improving an earlier
bound of O(n3)), and (3) in Markov decision processes (improving for m > n4/3
an earlier bound of O(min(m1.5, m·n2/3)). We also show that the same technique
can be used to compute the maximal end-component decomposition of a graph in time
O(n2), which is an improvement over earlier bounds for m > n4/3. 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.
alternative_title:
- IST Austria Technical Report
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. IST Austria; 2011. doi:10.15479/AT:IST-2011-0009
apa: Chatterjee, K., & Henzinger, M. H. (2011). An O(n2) time algorithm for
alternating Büchi games. IST Austria. https://doi.org/10.15479/AT:IST-2011-0009
chicago: Chatterjee, Krishnendu, and Monika H Henzinger. An O(N2) Time Algorithm
for Alternating Büchi Games. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0009.
ieee: K. Chatterjee and M. H. Henzinger, An O(n2) time algorithm for alternating
Büchi games. IST Austria, 2011.
ista: Chatterjee K, Henzinger MH. 2011. An O(n2) time algorithm for alternating
Büchi games, IST Austria, 20p.
mla: Chatterjee, Krishnendu, and Monika H. Henzinger. An O(N2) Time Algorithm
for Alternating Büchi Games. IST Austria, 2011, doi:10.15479/AT:IST-2011-0009.
short: K. Chatterjee, M.H. Henzinger, An O(N2) Time Algorithm for Alternating Büchi
Games, IST Austria, 2011.
date_created: 2018-12-12T11:38:59Z
date_published: 2011-07-11T00:00:00Z
date_updated: 2023-02-23T11:15:12Z
day: '11'
ddc:
- '000'
- '004'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2011-0009
file:
- access_level: open_access
checksum: 0b354264229045d982332fd2cb5b9a26
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:43Z
date_updated: 2020-07-14T12:46:39Z
file_id: '5504'
file_name: IST-2011-0009_IST-2011-0009.pdf
file_size: 388665
relation: main_file
file_date_updated: 2020-07-14T12:46:39Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '20'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '15'
related_material:
record:
- id: '3165'
relation: later_version
status: public
status: public
title: An O(n2) time algorithm for alternating Büchi games
type: technical_report
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2011'
...
---
_id: '5381'
abstract:
- lang: eng
text: "In two-player finite-state stochastic games of partial obser- vation on graphs,
in every state of the graph, the players simultaneously choose an action, and
their joint actions determine a probability distri- bution over the successor
states. The game is played for infinitely many rounds and thus the players construct
an infinite path in the graph. We consider reachability objectives where the first
player tries to ensure a target state to be visited almost-surely (i.e., with
probability 1) or pos- itively (i.e., with positive probability), no matter the
strategy of the second player.\r\n\r\nWe classify such games according to the
information and to the power of randomization available to the players. On the
basis of information, the game can be one-sided with either (a) player 1, or (b)
player 2 having partial observation (and the other player has perfect observation),
or two- sided with (c) both players having partial observation. On the basis of
randomization, (a) the players may not be allowed to use randomization (pure strategies),
or (b) they may choose a probability distribution over actions but the actual
random choice is external and not visible to the player (actions invisible), or
(c) they may use full randomization.\r\n\r\nOur main results for pure strategies
are as follows: (1) For one-sided games with player 2 perfect observation we show
that (in contrast to full randomized strategies) belief-based (subset-construction
based) strate- gies are not sufficient, and present an exponential upper bound
on mem- ory both for almost-sure and positive winning strategies; we show that
the problem of deciding the existence of almost-sure and positive winning strategies
for player 1 is EXPTIME-complete and present symbolic algo- rithms that avoid
the explicit exponential construction. (2) For one-sided games with player 1 perfect
observation we show that non-elementary memory is both necessary and sufficient
for both almost-sure and posi- tive winning strategies. (3) We show that for the
general (two-sided) case finite-memory strategies are sufficient for both positive
and almost-sure winning, and at least non-elementary memory is required. We establish
the equivalence of the almost-sure winning problems for pure strategies and for
randomized strategies with actions invisible. Our equivalence re- sult exhibit
serious flaws in previous results in the literature: we show a non-elementary
memory lower bound for almost-sure winning whereas an exponential upper bound
was previously claimed."
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: Laurent
full_name: Doyen, Laurent
last_name: Doyen
citation:
ama: 'Chatterjee K, Doyen L. Partial-Observation Stochastic Games: How to Win
When Belief Fails. IST Austria; 2011. doi:10.15479/AT:IST-2011-0007'
apa: 'Chatterjee, K., & Doyen, L. (2011). Partial-observation stochastic
games: How to win when belief fails. IST Austria. https://doi.org/10.15479/AT:IST-2011-0007'
chicago: 'Chatterjee, Krishnendu, and Laurent Doyen. Partial-Observation Stochastic
Games: How to Win When Belief Fails. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0007.'
ieee: 'K. Chatterjee and L. Doyen, Partial-observation stochastic games: How
to win when belief fails. IST Austria, 2011.'
ista: 'Chatterjee K, Doyen L. 2011. Partial-observation stochastic games: How to
win when belief fails, IST Austria, 43p.'
mla: 'Chatterjee, Krishnendu, and Laurent Doyen. Partial-Observation Stochastic
Games: How to Win When Belief Fails. IST Austria, 2011, doi:10.15479/AT:IST-2011-0007.'
short: 'K. Chatterjee, L. Doyen, Partial-Observation Stochastic Games: How to Win
When Belief Fails, IST Austria, 2011.'
date_created: 2018-12-12T11:39:00Z
date_published: 2011-07-05T00:00:00Z
date_updated: 2023-02-23T11:05:48Z
day: '05'
ddc:
- '000'
- '005'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2011-0007
file:
- access_level: open_access
checksum: 06bf6dfc97f6006e3fd0e9a3f31bc961
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:27Z
date_updated: 2020-07-14T12:46:39Z
file_id: '5488'
file_name: IST-2011-0007_IST-2011-0007.pdf
file_size: 574055
relation: main_file
file_date_updated: 2020-07-14T12:46:39Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '43'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '17'
related_material:
record:
- id: '1903'
relation: later_version
status: public
- id: '2211'
relation: later_version
status: public
- id: '2955'
relation: later_version
status: public
status: public
title: 'Partial-observation stochastic games: How to win when belief fails'
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5380'
abstract:
- lang: eng
text: 'We consider 2-player games played on a finite state space for an infinite
number of rounds. The games are concurrent: in each round, the two players (player
1 and player 2) choose their moves independently and simultaneously; the current
state and the two moves determine the successor state. We study concurrent games
with ω-regular winning conditions specified as parity objectives. We consider
the qualitative analysis problems: the computation of the almost-sure and limit-sure
winning set of states, where player 1 can ensure to win with probability 1 and
with probability arbitrarily close to 1, respectively. In general the almost-sure
and limit-sure winning strategies require both infinite-memory as well as infinite-precision
(to describe probabilities). We study the bounded-rationality problem for qualitative
analysis of concurrent parity games, where the strategy set for player 1 is restricted
to bounded-resource strategies. In terms of precision, strategies can be deterministic,
uniform, finite-precision or infinite-precision; and in terms of memory, strategies
can be memoryless, finite-memory or infinite-memory. We present a precise and
complete characterization of the qualitative winning sets for all combinations
of classes of strategies. In particular, we show that uniform memoryless strategies
are as powerful as finite-precision infinite-memory strategies, and infinite-precision
memoryless strategies are as powerful as infinite-precision finite-memory strategies. We
show that the winning sets can be computed in O(n2d+3) time, where n is the size
of the game structure and 2d is the number of priorities (or colors), and our
algorithms are symbolic. The membership problem of whether a state belongs to
a winning set can be decided in NP ∩ coNP. While this complexity is the same as
for the simpler class of turn-based parity games, where in each state only one
of the two players has a choice of moves, our algorithms,that are obtained by
characterization of the winning sets as μ-calculus formulas, are considerably
more involved than those for turn-based games.'
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
citation:
ama: Chatterjee K. Bounded Rationality in Concurrent Parity Games. IST Austria;
2011. doi:10.15479/AT:IST-2011-0008
apa: Chatterjee, K. (2011). Bounded rationality in concurrent parity games.
IST Austria. https://doi.org/10.15479/AT:IST-2011-0008
chicago: Chatterjee, Krishnendu. Bounded Rationality in Concurrent Parity Games.
IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0008.
ieee: K. Chatterjee, Bounded rationality in concurrent parity games. IST
Austria, 2011.
ista: Chatterjee K. 2011. Bounded rationality in concurrent parity games, IST Austria,
53p.
mla: Chatterjee, Krishnendu. Bounded Rationality in Concurrent Parity Games.
IST Austria, 2011, doi:10.15479/AT:IST-2011-0008.
short: K. Chatterjee, Bounded Rationality in Concurrent Parity Games, IST Austria,
2011.
date_created: 2018-12-12T11:39:00Z
date_published: 2011-07-11T00:00:00Z
date_updated: 2023-02-23T11:22:53Z
day: '11'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2011-0008
file:
- access_level: open_access
checksum: 0fd38186409be819a911c4990fa79d1f
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:54:22Z
date_updated: 2020-07-14T12:46:39Z
file_id: '5544'
file_name: IST-2011-0008_IST-2011-0008.pdf
file_size: 500399
relation: main_file
file_date_updated: 2020-07-14T12:46:39Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '53'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '16'
related_material:
record:
- id: '3338'
relation: later_version
status: public
status: public
title: Bounded rationality in concurrent parity games
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5382'
abstract:
- lang: eng
text: 'We consider two-player stochastic games played on a finite state space for
an infinite num- ber of rounds. The games are concurrent: in each round, the two
players (player 1 and player 2) choose their moves independently and simultaneously;
the current state and the two moves determine a probability distribution over
the successor states. We also consider the important special case of turn-based
stochastic games where players make moves in turns, rather than concurrently.
We study concurrent games with ω-regular winning conditions specified as parity
objectives. The value for player 1 for a parity objective is the maximal probability
with which the player can guarantee the satisfaction of the objective against
all strategies of the opponent. We study the problem of continuity and robustness
of the value function in concurrent and turn-based stochastic parity games with
respect to imprecision in the transition probabilities. We present quantitative
bounds on the difference of the value function (in terms of the imprecision of
the transition probabilities) and show the value continuity for structurally equivalent
concurrent games (two games are structurally equivalent if the support of the
transition func- tion is same and the probabilities differ). We also show robustness
of optimal strategies for structurally equivalent turn-based stochastic parity
games. Finally we show that the value continuity property breaks without the structurally
equivalent assumption (even for Markov chains) and show that our quantitative
bound is asymptotically optimal. Hence our results are tight (the assumption is
both necessary and sufficient) and optimal (our quantitative bound is asymptotically
optimal).'
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
citation:
ama: Chatterjee K. Robustness of Structurally Equivalent Concurrent Parity Games.
IST Austria; 2011. doi:10.15479/AT:IST-2011-0006
apa: Chatterjee, K. (2011). Robustness of structurally equivalent concurrent
parity games. IST Austria. https://doi.org/10.15479/AT:IST-2011-0006
chicago: Chatterjee, Krishnendu. Robustness of Structurally Equivalent Concurrent
Parity Games. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0006.
ieee: K. Chatterjee, Robustness of structurally equivalent concurrent parity
games. IST Austria, 2011.
ista: Chatterjee K. 2011. Robustness of structurally equivalent concurrent parity
games, IST Austria, 18p.
mla: Chatterjee, Krishnendu. Robustness of Structurally Equivalent Concurrent
Parity Games. IST Austria, 2011, doi:10.15479/AT:IST-2011-0006.
short: K. Chatterjee, Robustness of Structurally Equivalent Concurrent Parity Games,
IST Austria, 2011.
date_created: 2018-12-12T11:39:00Z
date_published: 2011-06-27T00:00:00Z
date_updated: 2023-02-23T11:23:01Z
day: '27'
ddc:
- '000'
- '005'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2011-0006
file:
- access_level: open_access
checksum: 1322b652d6ab07eb5248298a3f91c1cf
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:54:24Z
date_updated: 2020-07-14T12:46:40Z
file_id: '5546'
file_name: IST-2011-0006_IST-2011-0006.pdf
file_size: 335997
relation: main_file
file_date_updated: 2020-07-14T12:46:40Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: '18'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '18'
related_material:
record:
- id: '3341'
relation: later_version
status: public
status: public
title: Robustness of structurally equivalent concurrent parity games
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5385'
abstract:
- lang: eng
text: There is recently a significant effort to add quantitative objectives to formal
verification and synthesis. We introduce and investigate the extension of temporal
logics with quantitative atomic assertions, aiming for a general and flexible
framework for quantitative-oriented specifications. In the heart of quantitative
objectives lies the accumulation of values along a computation. It is either the
accumulated summation, as with the energy objectives, or the accumulated average,
as with the mean-payoff objectives. We investigate the extension of temporal logics
with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is
a numeric variable of the system, c is a constant rational number, and Sum(v)
and Avg(v) denote the accumulated sum and average of the values of v from the
beginning of the computation up to the current point of time. We also allow the
path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring
to the average value along an entire computation. We study the border of decidability
for extensions of various temporal logics. In particular, we show that extending
the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by
prefix-accumulation assertions and extending LTL with path-accumulation assertions,
result in temporal logics whose model-checking problem is decidable. The extended
logics allow to significantly extend the currently known energy and mean-payoff
objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”,
allowing, for example, to specify constraints on the average waiting time between
a request and a grant. On the negative side, we show that the fragment we point
to is, in a sense, the maximal logic whose extension with prefix-accumulation
assertions permits a decidable model-checking procedure. Extending a temporal
logic that has the EG or EU modalities, and in particular CTL and LTL, makes the
problem undecidable.
alternative_title:
- IST Austria Technical Report
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- 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: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: Boker U, Chatterjee K, Henzinger TA, Kupferman O. Temporal Specifications
with Accumulative Values. IST Austria; 2011. doi:10.15479/AT:IST-2011-0003
apa: Boker, U., Chatterjee, K., Henzinger, T. A., & Kupferman, O. (2011). Temporal
specifications with accumulative values. IST Austria. https://doi.org/10.15479/AT:IST-2011-0003
chicago: Boker, Udi, Krishnendu Chatterjee, Thomas A Henzinger, and Orna Kupferman.
Temporal Specifications with Accumulative Values. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0003.
ieee: U. Boker, K. Chatterjee, T. A. Henzinger, and O. Kupferman, Temporal specifications
with accumulative values. IST Austria, 2011.
ista: Boker U, Chatterjee K, Henzinger TA, Kupferman O. 2011. Temporal specifications
with accumulative values, IST Austria, 14p.
mla: Boker, Udi, et al. Temporal Specifications with Accumulative Values.
IST Austria, 2011, doi:10.15479/AT:IST-2011-0003.
short: U. Boker, K. Chatterjee, T.A. Henzinger, O. Kupferman, Temporal Specifications
with Accumulative Values, IST Austria, 2011.
date_created: 2018-12-12T11:39:02Z
date_published: 2011-04-04T00:00:00Z
date_updated: 2023-02-23T11:23:41Z
day: '04'
ddc:
- '000'
- '004'
department:
- _id: ToHe
- _id: KrCh
doi: 10.15479/AT:IST-2011-0003
ec_funded: 1
file:
- access_level: open_access
checksum: 8491d0d48c4911620ecd5350b413c11e
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:00Z
date_updated: 2020-07-14T12:46:41Z
file_id: '5461'
file_name: IST-2011-0003_IST-2011-0003.pdf
file_size: 366281
relation: main_file
file_date_updated: 2020-07-14T12:46:41Z
has_accepted_license: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: '14'
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25F1337C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '214373'
name: Design for Embedded Systems
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '21'
related_material:
record:
- id: '2038'
relation: later_version
status: public
- id: '3356'
relation: later_version
status: public
status: public
title: Temporal specifications with accumulative values
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...