---
_id: '2716'
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 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 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: "Krishnendu Chatterjee is supported by Austrian Science Fund (FWF)
  Grant No P 23499-N23, FWF NFN Grant No S11407 (RiSE), ERC Starting Grant (279307:
  Graph Games) and Microsoft faculty fellowship. Mickael Randour is supported by F.R.S.-FNRS.
  fellowship. \r\nJean-François Raskin is supported by ERC Starting Grant (279499:
  inVEST).Thanks to D. Sbabo for useful pointers, V. Bruyère for comments on a preliminary
  draft, and A. Bohy for fruitful discussions about the Acacia+ tool. We are grateful
  to the anonymous reviewers for their insightful comments. "
article_processing_charge: No
article_type: original
arxiv: 1
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
  full_name: Raskin, Jean
  last_name: Raskin
citation:
  ama: Chatterjee K, Randour M, Raskin J. Strategy synthesis for multi-dimensional
    quantitative objectives. <i>Acta Informatica</i>. 2014;51(3-4):129-163. doi:<a
    href="https://doi.org/10.1007/s00236-013-0182-6">10.1007/s00236-013-0182-6</a>
  apa: Chatterjee, K., Randour, M., &#38; Raskin, J. (2014). Strategy synthesis for
    multi-dimensional quantitative objectives. <i>Acta Informatica</i>. Springer.
    <a href="https://doi.org/10.1007/s00236-013-0182-6">https://doi.org/10.1007/s00236-013-0182-6</a>
  chicago: Chatterjee, Krishnendu, Mickael Randour, and Jean Raskin. “Strategy Synthesis
    for Multi-Dimensional Quantitative Objectives.” <i>Acta Informatica</i>. Springer,
    2014. <a href="https://doi.org/10.1007/s00236-013-0182-6">https://doi.org/10.1007/s00236-013-0182-6</a>.
  ieee: K. Chatterjee, M. Randour, and J. Raskin, “Strategy synthesis for multi-dimensional
    quantitative objectives,” <i>Acta Informatica</i>, vol. 51, no. 3–4. Springer,
    pp. 129–163, 2014.
  ista: Chatterjee K, Randour M, Raskin J. 2014. Strategy synthesis for multi-dimensional
    quantitative objectives. Acta Informatica. 51(3–4), 129–163.
  mla: Chatterjee, Krishnendu, et al. “Strategy Synthesis for Multi-Dimensional Quantitative
    Objectives.” <i>Acta Informatica</i>, vol. 51, no. 3–4, Springer, 2014, pp. 129–63,
    doi:<a href="https://doi.org/10.1007/s00236-013-0182-6">10.1007/s00236-013-0182-6</a>.
  short: K. Chatterjee, M. Randour, J. Raskin, Acta Informatica 51 (2014) 129–163.
date_created: 2018-12-11T11:59:14Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-09-29T11:10:44Z
day: '01'
department:
- _id: KrCh
doi: 10.1007/s00236-013-0182-6
external_id:
  arxiv:
  - '1201.5073'
  isi:
  - '000335981500002'
intvolume: '        51'
isi: 1
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1201.5073
month: '06'
oa: 1
oa_version: Preprint
page: 129 - 163
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S11407
  name: Game Theory
publication: Acta Informatica
publication_status: published
publisher: Springer
publist_id: '4176'
quality_controlled: '1'
related_material:
  record:
  - id: '10904'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: Strategy synthesis for multi-dimensional quantitative objectives
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 51
year: '2014'
...