---
_id: '10904'
abstract:
- lang: eng
text: Multi-dimensional mean-payoff and energy games provide the mathematical foundation
for the quantitative study of reactive systems, and play a central role in the
emerging quantitative theory of verification and synthesis. In this work, we study
the strategy synthesis problem for games with such multi-dimensional objectives
along with a parity condition, a canonical way to express ω-regular conditions.
While in general, the winning strategies in such games may require infinite memory,
for synthesis the most relevant problem is the construction of a finite-memory
winning strategy (if one exists). Our main contributions are as follows. First,
we show a tight exponential bound (matching upper and lower bounds) on the memory
required for finite-memory winning strategies in both multi-dimensional mean-payoff
and energy games along with parity objectives. This significantly improves the
triple exponential upper bound for multi energy games (without parity) that could
be derived from results in literature for games on VASS (vector addition systems
with states). Second, we present an optimal symbolic and incremental algorithm
to compute a finite-memory winning strategy (if one exists) in such games. Finally,
we give a complete characterization of when finite memory of strategies can be
traded off for randomness. In particular, we show that for one-dimension mean-payoff
parity games, randomized memoryless strategies are as powerful as their pure finite-memory
counterparts.
acknowledgement: 'Author supported by Austrian Science Fund (FWF) Grant No P 23499-N23,
FWF NFN Grant No S11407 (RiSE), ERC Start Grant (279307: Graph Games), Microsoft
faculty fellowship.'
alternative_title:
- LNCS
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: Mickael
full_name: Randour, Mickael
last_name: Randour
- first_name: Jean-François
full_name: Raskin, Jean-François
last_name: Raskin
citation:
ama: 'Chatterjee K, Randour M, Raskin J-F. Strategy synthesis for multi-dimensional
quantitative objectives. In: Koutny M, Ulidowski I, eds. CONCUR 2012 - Concurrency
Theory. Vol 7454. Berlin, Heidelberg: Springer; 2012:115-131. doi:10.1007/978-3-642-32940-1_10'
apa: 'Chatterjee, K., Randour, M., & Raskin, J.-F. (2012). Strategy synthesis
for multi-dimensional quantitative objectives. In M. Koutny & I. Ulidowski
(Eds.), CONCUR 2012 - Concurrency Theory (Vol. 7454, pp. 115–131). Berlin,
Heidelberg: Springer. https://doi.org/10.1007/978-3-642-32940-1_10'
chicago: 'Chatterjee, Krishnendu, Mickael Randour, and Jean-François Raskin. “Strategy
Synthesis for Multi-Dimensional Quantitative Objectives.” In CONCUR 2012 -
Concurrency Theory, edited by Maciej Koutny and Irek Ulidowski, 7454:115–31.
Berlin, Heidelberg: Springer, 2012. https://doi.org/10.1007/978-3-642-32940-1_10.'
ieee: K. Chatterjee, M. Randour, and J.-F. Raskin, “Strategy synthesis for multi-dimensional
quantitative objectives,” in CONCUR 2012 - Concurrency Theory, Newcastle
upon Tyne, United Kingdom, 2012, vol. 7454, pp. 115–131.
ista: 'Chatterjee K, Randour M, Raskin J-F. 2012. Strategy synthesis for multi-dimensional
quantitative objectives. CONCUR 2012 - Concurrency Theory. CONCUR: Conference
on Concurrency Theory, LNCS, vol. 7454, 115–131.'
mla: Chatterjee, Krishnendu, et al. “Strategy Synthesis for Multi-Dimensional Quantitative
Objectives.” CONCUR 2012 - Concurrency Theory, edited by Maciej Koutny
and Irek Ulidowski, vol. 7454, Springer, 2012, pp. 115–31, doi:10.1007/978-3-642-32940-1_10.
short: K. Chatterjee, M. Randour, J.-F. Raskin, in:, M. Koutny, I. Ulidowski (Eds.),
CONCUR 2012 - Concurrency Theory, Springer, Berlin, Heidelberg, 2012, pp. 115–131.
conference:
end_date: 2012-09-07
location: Newcastle upon Tyne, United Kingdom
name: 'CONCUR: Conference on Concurrency Theory'
start_date: 2012-09-04
date_created: 2022-03-21T08:00:21Z
date_published: 2012-09-15T00:00:00Z
date_updated: 2023-02-23T10:55:06Z
day: '15'
department:
- _id: KrCh
doi: 10.1007/978-3-642-32940-1_10
ec_funded: 1
editor:
- first_name: Maciej
full_name: Koutny, Maciej
last_name: Koutny
- first_name: Irek
full_name: Ulidowski, Irek
last_name: Ulidowski
external_id:
arxiv:
- '1201.5073'
intvolume: ' 7454'
language:
- iso: eng
month: '09'
oa_version: Preprint
page: 115-131
place: Berlin, Heidelberg
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: CONCUR 2012 - Concurrency Theory
publication_identifier:
eisbn:
- '9783642329401'
isbn:
- '9783642329395'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer
quality_controlled: '1'
related_material:
record:
- id: '2716'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Strategy synthesis for multi-dimensional quantitative objectives
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7454
year: '2012'
...