---
_id: '523'
abstract:
- lang: eng
text: We consider two-player games played on weighted directed graphs with mean-payoff
and total-payoff objectives, two classical quantitative objectives. While for
single-dimensional games the complexity and memory bounds for both objectives
coincide, we show that in contrast to multi-dimensional mean-payoff games that
are known to be coNP-complete, multi-dimensional total-payoff games are undecidable.
We introduce conservative approximations of these objectives, where the payoff
is considered over a local finite window sliding along a play, instead of the
whole play. For single dimension, we show that (i) if the window size is polynomial,
deciding the winner takes polynomial time, and (ii) the existence of a bounded
window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff
games. For multiple dimensions, we show that (i) the problem with fixed window
size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to
decide the existence of a bounded window.
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
- first_name: Mickael
full_name: Randour, Mickael
last_name: Randour
- first_name: Jean
full_name: Raskin, Jean
last_name: Raskin
citation:
ama: Chatterjee K, Doyen L, Randour M, Raskin J. Looking at mean-payoff and total-payoff
through windows. *Information and Computation*. 2015;242(6):25-52. doi:10.1016/j.ic.2015.03.010
apa: Chatterjee, K., Doyen, L., Randour, M., & Raskin, J. (2015). Looking at
mean-payoff and total-payoff through windows. *Information and Computation*,
*242*(6), 25–52. https://doi.org/10.1016/j.ic.2015.03.010
chicago: 'Chatterjee, Krishnendu, Laurent Doyen, Mickael Randour, and Jean Raskin.
“Looking at Mean-Payoff and Total-Payoff through Windows.” *Information and
Computation* 242, no. 6 (2015): 25–52. https://doi.org/10.1016/j.ic.2015.03.010.'
ieee: K. Chatterjee, L. Doyen, M. Randour, and J. Raskin, “Looking at mean-payoff
and total-payoff through windows,” *Information and Computation*, vol. 242,
no. 6, pp. 25–52, 2015.
ista: Chatterjee K, Doyen L, Randour M, Raskin J. 2015. Looking at mean-payoff and
total-payoff through windows. Information and Computation. 242(6), 25–52.
mla: Chatterjee, Krishnendu, et al. “Looking at Mean-Payoff and Total-Payoff through
Windows.” *Information and Computation*, vol. 242, no. 6, Elsevier, 2015,
pp. 25–52, doi:10.1016/j.ic.2015.03.010.
short: K. Chatterjee, L. Doyen, M. Randour, J. Raskin, Information and Computation
242 (2015) 25–52.
date_created: 2018-12-11T11:46:57Z
date_published: 2015-03-24T00:00:00Z
date_updated: 2020-08-11T10:10:18Z
day: '24'
department:
- _id: KrCh
doi: 10.1016/j.ic.2015.03.010
ec_funded: 1
intvolume: ' 242'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1302.4248
month: '03'
oa: 1
oa_version: Preprint
page: 25 - 52
project:
- _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
- _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: Information and Computation
publication_status: published
publisher: Elsevier
publist_id: '7296'
quality_controlled: '1'
related_material:
record:
- id: '2279'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Looking at mean-payoff and total-payoff through windows
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 242
year: '2015'
...
---
_id: '524'
abstract:
- lang: eng
text: 'We consider concurrent games played by two players on a finite-state graph,
where in every round the players simultaneously choose a move, and the current
state along with the joint moves determine the successor state. We study the most
fundamental objective for concurrent games, namely, mean-payoff or limit-average
objective, where a reward is associated to each transition, and the goal of player
1 is to maximize the long-run average of the rewards, and the objective of player
2 is strictly the opposite (i.e., the games are zero-sum). The path constraint
for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward,
or arbitrarily close to it; or quantitative, i.e., a given threshold between the
minimal and maximal reward. We consider the computation of the almost-sure (resp.
positive) winning sets, where player 1 can ensure that the path constraint is
satisfied with probability 1 (resp. positive probability). Almost-sure winning
with qualitative constraint exactly corresponds to the question of whether there
exists a strategy to ensure that the payoff is the maximal reward of the game.
Our main results for qualitative path constraints are as follows: (1) we establish
qualitative determinacy results that show that for every state either player 1
has a strategy to ensure almost-sure (resp. positive) winning against all player-2
strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp.
positive) winning against all player-1 strategies; (2) we present optimal strategy
complexity results that precisely characterize the classes of strategies required
for almost-sure and positive winning for both players; and (3) we present quadratic
time algorithms to compute the almost-sure and the positive winning sets, matching
the best known bound of the algorithms for much simpler problems (such as reachability
objectives). For quantitative constraints we show that a polynomial time solution
for the almost-sure or the positive winning set would imply a solution to a long-standing
open problem (of solving the value problem of turn-based deterministic mean-payoff
games) that is not known to be solvable in polynomial time.'
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
citation:
ama: Chatterjee K, Ibsen-Jensen R. Qualitative analysis of concurrent mean payoff
games. *Information and Computation*. 2015;242(6):2-24. doi:10.1016/j.ic.2015.03.009
apa: Chatterjee, K., & Ibsen-Jensen, R. (2015). Qualitative analysis of concurrent
mean payoff games. *Information and Computation*, *242*(6), 2–24. https://doi.org/10.1016/j.ic.2015.03.009
chicago: 'Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “Qualitative Analysis
of Concurrent Mean Payoff Games.” *Information and Computation* 242, no.
6 (2015): 2–24. https://doi.org/10.1016/j.ic.2015.03.009.'
ieee: K. Chatterjee and R. Ibsen-Jensen, “Qualitative analysis of concurrent mean
payoff games,” *Information and Computation*, vol. 242, no. 6, pp. 2–24,
2015.
ista: Chatterjee K, Ibsen-Jensen R. 2015. Qualitative analysis of concurrent mean
payoff games. Information and Computation. 242(6), 2–24.
mla: Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “Qualitative Analysis of Concurrent
Mean Payoff Games.” *Information and Computation*, vol. 242, no. 6, Elsevier,
2015, pp. 2–24, doi:10.1016/j.ic.2015.03.009.
short: K. Chatterjee, R. Ibsen-Jensen, Information and Computation 242 (2015) 2–24.
date_created: 2018-12-11T11:46:57Z
date_published: 2015-10-11T00:00:00Z
date_updated: 2020-08-11T10:10:18Z
day: '11'
department:
- _id: KrCh
doi: 10.1016/j.ic.2015.03.009
external_id:
arxiv:
- '1409.5306'
intvolume: ' 242'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1409.5306
month: '10'
oa: 1
oa_version: Preprint
page: 2 - 24
publication: Information and Computation
publication_status: published
publisher: Elsevier
publist_id: '7295'
quality_controlled: '1'
related_material:
record:
- id: '5403'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Qualitative analysis of concurrent mean payoff games
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 242
year: '2015'
...
---
_id: '5429'
abstract:
- lang: eng
text: "We consider Markov decision processes (MDPs) with multiple limit-average
(or mean-payoff) objectives. \r\nThere have been two different views: (i) the
expectation semantics, where the goal is to optimize the expected mean-payoff
objective, and (ii) the satisfaction semantics, where the goal is to maximize
the probability of runs such that the mean-payoff value stays above a given vector.
\ \r\nWe consider the problem where the goal is to optimize the expectation under
the constraint that the satisfaction semantics is ensured, and thus consider a
generalization that unifies the existing semantics.\r\nOur problem captures the
notion of optimization with respect to strategies that are risk-averse (i.e.,
ensures certain probabilistic guarantee).\r\nOur main results are algorithms for
the decision problem which are always polynomial in the size of the MDP. We also
show that an approximation of the Pareto-curve can be computed in time polynomial
in the size of the MDP, and the approximation factor, but exponential in the number
of dimensions.\r\nFinally, we present a complete characterization of the strategy
complexity (in terms of memory bounds and randomization) required to solve our
problem."
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: Zuzana
full_name: Komarkova, Zuzana
last_name: Komarkova
- first_name: Jan
full_name: Kretinsky, Jan
id: 44CEF464-F248-11E8-B48F-1D18A9856A87
last_name: Kretinsky
orcid: 0000-0002-8122-2881
citation:
ama: Chatterjee K, Komarkova Z, Kretinsky J. *Unifying Two Views on Multiple Mean-Payoff
Objectives in Markov Decision Processes*. IST Austria; 2015. doi:10.15479/AT:IST-2015-318-v1-1
apa: Chatterjee, K., Komarkova, Z., & Kretinsky, J. (2015). *Unifying two
views on multiple mean-payoff objectives in Markov decision processes*. IST
Austria. https://doi.org/10.15479/AT:IST-2015-318-v1-1
chicago: Chatterjee, Krishnendu, Zuzana Komarkova, and Jan Kretinsky. *Unifying
Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes*.
IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-318-v1-1.
ieee: K. Chatterjee, Z. Komarkova, and J. Kretinsky, *Unifying two views on multiple
mean-payoff objectives in Markov decision processes*. IST Austria, 2015.
ista: Chatterjee K, Komarkova Z, Kretinsky J. 2015. Unifying two views on multiple
mean-payoff objectives in Markov decision processes, IST Austria, 41p.
mla: Chatterjee, Krishnendu, et al. *Unifying Two Views on Multiple Mean-Payoff
Objectives in Markov Decision Processes*. IST Austria, 2015, doi:10.15479/AT:IST-2015-318-v1-1.
short: K. Chatterjee, Z. Komarkova, J. Kretinsky, Unifying Two Views on Multiple
Mean-Payoff Objectives in Markov Decision Processes, IST Austria, 2015.
date_created: 2018-12-12T11:39:17Z
date_published: 2015-01-12T00:00:00Z
date_updated: 2020-08-11T10:10:15Z
day: '12'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2015-318-v1-1
file:
- access_level: open_access
checksum: e4869a584567c506349abda9c8ec7db3
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:54:11Z
date_updated: 2020-07-14T12:46:52Z
file_id: '5533'
file_name: IST-2015-318-v1+1_main.pdf
file_size: 689863
relation: main_file
file_date_updated: 2020-07-14T12:46:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: '41'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '318'
related_material:
record:
- id: '5435'
relation: later_version
status: public
- id: '1657'
relation: later_version
status: public
- id: '466'
relation: later_version
status: public
status: public
title: Unifying two views on multiple mean-payoff objectives in Markov decision processes
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '5430'
abstract:
- lang: eng
text: We consider the core algorithmic problems related to verification of systems
with respect to three classical quantitative properties, namely, the mean- payoff
property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute
the optimal value (the infimum value over all traces) from every node of the graph.
We consider graphs with constant treewidth, and it is well-known that the control-flow
graphs of most programs have constant treewidth. Let n denote the number of nodes
of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) )
and W the largest absolute value of the weights. Our main theoretical results
are as follows. First, for constant treewidth graphs we present an algorithm that
approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time
O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms
that require quadratic time. Second, for the ratio property we present an algorithm
that for constant treewidth graphs works in time O ( n · log( | a · b · n | ))
= O ( n · log( n · W )) , when the output is a b , as compared to the previously
best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the
minimum initial credit problem we show that (i) for general graphs the problem
can be solved in O ( n 2 · m ) time and the associated decision problem can be
solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n
· W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth
graphs we present an algorithm that requires O ( n · log n ) time, improving the
previous known O ( n 4 · log( n · W )) bound. We have implemented some of our
algorithms and show that they present a significant speedup on standard benchmarks.
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: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
- first_name: Andreas
full_name: Pavlogiannis, Andreas
id: 49704004-F248-11E8-B48F-1D18A9856A87
last_name: Pavlogiannis
citation:
ama: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. *Faster Algorithms for Quantitative
Verification in Constant Treewidth Graphs*. IST Austria; 2015. doi:10.15479/AT:IST-2015-319-v1-1
apa: Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). *Faster
algorithms for quantitative verification in constant treewidth graphs*. IST
Austria. https://doi.org/10.15479/AT:IST-2015-319-v1-1
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis.
*Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs*.
IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-319-v1-1.
ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, *Faster algorithms
for quantitative verification in constant treewidth graphs*. IST Austria, 2015.
ista: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for
quantitative verification in constant treewidth graphs, IST Austria, 31p.
mla: Chatterjee, Krishnendu, et al. *Faster Algorithms for Quantitative Verification
in Constant Treewidth Graphs*. IST Austria, 2015, doi:10.15479/AT:IST-2015-319-v1-1.
short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative
Verification in Constant Treewidth Graphs, IST Austria, 2015.
date_created: 2018-12-12T11:39:17Z
date_published: 2015-02-10T00:00:00Z
date_updated: 2020-08-11T10:09:21Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2015-319-v1-1
file:
- access_level: open_access
checksum: 62c6ea01e342553dcafb88a070fb1ad5
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:21Z
date_updated: 2020-07-14T12:46:52Z
file_id: '5482'
file_name: IST-2015-319-v1+1_long.pdf
file_size: 1089651
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file_date_updated: 2020-07-14T12:46:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '31'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '319'
related_material:
record:
- id: '5437'
relation: later_version
status: public
- id: '1607'
relation: later_version
status: public
status: public
title: Faster algorithms for quantitative verification in constant treewidth graphs
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '5431'
abstract:
- lang: eng
text: "We consider finite-state concurrent stochastic games, played by k>=2 players
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. We consider reachability objectives that given a target set
of states require that some state in the target set is visited, and the dual safety
objectives that given a target set require that only states in the target set
are 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.\r\n\r\n Our main results are as follows: We show that in two-player
zero-sum concurrent stochastic games (with reachability objective for one player
and the complementary safety objective for the other player): (i) the optimal
bound on the patience of optimal and epsilon-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. In general we study
the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that
if there is at least one player with reachability objective, then doubly-exponential
patience is needed in general for epsilon-Nash equilibrium strategies, whereas
in contrast if all players have safety objectives, then the optimal bound on patience
for epsilon-Nash equilibrium strategies is only exponential."
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: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
- first_name: Kristoffer
full_name: Hansen, Kristoffer
last_name: Hansen
citation:
ama: Chatterjee K, Ibsen-Jensen R, Hansen K. *The Patience of Concurrent Stochastic
Games with Safety and Reachability Objectives*. IST Austria; 2015. doi:10.15479/AT:IST-2015-322-v1-1
apa: Chatterjee, K., Ibsen-Jensen, R., & Hansen, K. (2015). *The patience
of concurrent stochastic games with safety and reachability objectives*. IST
Austria. https://doi.org/10.15479/AT:IST-2015-322-v1-1
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Kristoffer Hansen. *The
Patience of Concurrent Stochastic Games with Safety and Reachability Objectives*.
IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-322-v1-1.
ieee: K. Chatterjee, R. Ibsen-Jensen, and K. Hansen, *The patience of concurrent
stochastic games with safety and reachability objectives*. IST Austria, 2015.
ista: Chatterjee K, Ibsen-Jensen R, Hansen K. 2015. The patience of concurrent stochastic
games with safety and reachability objectives, IST Austria, 25p.
mla: Chatterjee, Krishnendu, et al. *The Patience of Concurrent Stochastic Games
with Safety and Reachability Objectives*. IST Austria, 2015, doi:10.15479/AT:IST-2015-322-v1-1.
short: K. Chatterjee, R. Ibsen-Jensen, K. Hansen, The Patience of Concurrent Stochastic
Games with Safety and Reachability Objectives, IST Austria, 2015.
date_created: 2018-12-12T11:39:17Z
date_published: 2015-02-19T00:00:00Z
date_updated: 2020-07-14T23:07:59Z
day: '19'
ddc:
- '005'
- '519'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2015-322-v1-1
file:
- access_level: open_access
checksum: bfb858262c30445b8e472c40069178a2
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:31Z
date_updated: 2020-07-14T12:46:53Z
file_id: '5491'
file_name: IST-2015-322-v1+1_safetygames.pdf
file_size: 661015
relation: main_file
file_date_updated: 2020-07-14T12:46:53Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '25'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '322'
status: public
title: The patience of concurrent stochastic games with safety and reachability objectives
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...