---
_id: '2329'
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 both finite-state game graphs, and recursive game graphs (or
pushdown game graphs) that model the control flow of sequential programs with
recursion. The objectives we study are multidimensional mean-payoff objectives,
where the goal of player 1 is to ensure that the mean-payoff is non-negative in
all dimensions. 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.
Our main contributions are as follows: (1) We show that finite-state multidimensional
mean-payoff games can be solved in polynomial time if the number of dimensions
and the maximal absolute value of the weights are fixed; whereas if the number
of dimensions is arbitrary, then the problem is known to be coNP-complete. (2)
We show that pushdown graphs with multidimensional mean-payoff objectives can
be solved in polynomial time. For both (1) and (2) our algorithms are based on
hyperplane separation technique. (3) For pushdown games under global strategies
both one and multidimensional mean-payoff objectives problems are known to be
undecidable, and we show that under modular strategies the multidimensional problem
is also undecidable; under modular strategies the one-dimensional problem is NP-complete.
We show that if the number of modules, the number of exits, and the maximal absolute
value of the weights are fixed, then pushdown games under modular strategies with
one-dimensional mean-payoff objectives can be solved in polynomial time, and if
either the number of exits or the number of modules is unbounded, then the problem
is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for
finite-state multidimensional mean-payoff games or pushdown games under modular
strategies with one-dimensional mean-payoff objectives would imply the fixed parameter
tractability of parity games.'
alternative_title:
- LNCS
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. Hyperplane separation technique for multidimensional
mean-payoff games. 2013;8052:500-515. doi:10.1007/978-3-642-40184-8_35
apa: 'Chatterjee, K., & Velner, Y. (2013). Hyperplane separation technique for
multidimensional mean-payoff games. Presented at the CONCUR: Concurrency Theory,
Buenos Aires, Argentinia: Springer. https://doi.org/10.1007/978-3-642-40184-8_35'
chicago: Chatterjee, Krishnendu, and Yaron Velner. “Hyperplane Separation Technique
for Multidimensional Mean-Payoff Games.” Lecture Notes in Computer Science. Springer,
2013. https://doi.org/10.1007/978-3-642-40184-8_35.
ieee: K. Chatterjee and Y. Velner, “Hyperplane separation technique for multidimensional
mean-payoff games,” vol. 8052. Springer, pp. 500–515, 2013.
ista: Chatterjee K, Velner Y. 2013. Hyperplane separation technique for multidimensional
mean-payoff games. 8052, 500–515.
mla: Chatterjee, Krishnendu, and Yaron Velner. Hyperplane Separation Technique
for Multidimensional Mean-Payoff Games. Vol. 8052, Springer, 2013, pp. 500–15,
doi:10.1007/978-3-642-40184-8_35.
short: K. Chatterjee, Y. Velner, 8052 (2013) 500–515.
conference:
end_date: 2013-08-30
location: Buenos Aires, Argentinia
name: 'CONCUR: Concurrency Theory'
start_date: 2013-08-27
date_created: 2018-12-11T11:57:01Z
date_published: 2013-08-01T00:00:00Z
date_updated: 2023-02-23T13:00:42Z
day: '01'
department:
- _id: KrCh
doi: 10.1007/978-3-642-40184-8_35
ec_funded: 1
external_id:
arxiv:
- '1210.3141'
intvolume: ' 8052'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1210.3141
month: '08'
oa: 1
oa_version: Preprint
page: 500 - 515
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_status: published
publisher: Springer
publist_id: '4597'
quality_controlled: '1'
related_material:
record:
- id: '717'
relation: later_version
status: public
scopus_import: 1
series_title: Lecture Notes in Computer Science
status: public
title: Hyperplane separation technique for multidimensional mean-payoff games
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8052
year: '2013'
...