---
_id: '4628'
abstract:
- lang: eng
  text: 'Discounting the future means that the value, today, of a unit payoffis 1
    if the payoffo ccurs today, a if it occurs tomorrow, a 2 if it occurs the day
    after tomorrow, and so on, for some real-valued discount factor 0 < a <
    1. Discounting (or inflation) is a key paradigm in economics and has been studied
    in Markov decision processes as well as game theory. We submit that discounting
    also has a natural place in systems engineering: for nonterminating systems, a
    potential bug in the far-away future is less troubling than a potential bug today.
    We therefore develop a systems theory with discounting. Our theory includes several
    basic elements: discounted versions of system properties that correspond to the
    ω-regular properties, fixpoint-based algorithms for checking discounted properties,
    and a quantitative notion of bisimilarity for capturing the difference between
    two states with respect to discounted properties. We present the theory in a general
    form that applies to probabilistic systems as well as multicomponent systems (games),
    but it readily specializes to classical transition systems. We show that discounting,
    besides its natural practical appeal, has also several mathematical benefits.
    First, the resulting theory is robust, in that small perturbations of a system
    can cause only small changes in the properties of the system. Second, the theory
    is computational, in that the values of discounted properties, as well as the
    discounted bisimilarity distance between states, can be computed to any desired
    degree of precision.'
acknowledgement: This research was supported in part by the NSF CAREER award CCR-0132780,
  the DARPA grant F33615-C-98-3614, the NSF grants CCR-9988172, CCR-0234690 and CCR-0225610,
  and the ONR grant N00014-02-1-0671.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Luca
  full_name: De Alfaro, Luca
  last_name: De Alfaro
- 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: Ritankar
  full_name: Majumdar, Ritankar
  last_name: Majumdar
citation:
  ama: 'De Alfaro L, Henzinger TA, Majumdar R. Discounting the future in systems theory.
    In: <i>Proceedings of the 30th International Colloquium on Automata, Languages
    and Programming</i>. Vol 2719. Springer; 2003:1022-1037. doi:<a href="https://doi.org/10.1007/3-540-45061-0_79">10.1007/3-540-45061-0_79</a>'
  apa: 'De Alfaro, L., Henzinger, T. A., &#38; Majumdar, R. (2003). Discounting the
    future in systems theory. In <i>Proceedings of the 30th International Colloquium
    on Automata, Languages and Programming</i> (Vol. 2719, pp. 1022–1037). Eindhoven,
    The Netherlands: Springer. <a href="https://doi.org/10.1007/3-540-45061-0_79">https://doi.org/10.1007/3-540-45061-0_79</a>'
  chicago: De Alfaro, Luca, Thomas A Henzinger, and Ritankar Majumdar. “Discounting
    the Future in Systems Theory.” In <i>Proceedings of the 30th International Colloquium
    on Automata, Languages and Programming</i>, 2719:1022–37. Springer, 2003. <a href="https://doi.org/10.1007/3-540-45061-0_79">https://doi.org/10.1007/3-540-45061-0_79</a>.
  ieee: L. De Alfaro, T. A. Henzinger, and R. Majumdar, “Discounting the future in
    systems theory,” in <i>Proceedings of the 30th International Colloquium on Automata,
    Languages and Programming</i>, Eindhoven, The Netherlands, 2003, vol. 2719, pp.
    1022–1037.
  ista: 'De Alfaro L, Henzinger TA, Majumdar R. 2003. Discounting the future in systems
    theory. Proceedings of the 30th International Colloquium on Automata, Languages
    and Programming. ICALP: Automata, Languages and Programming, LNCS, vol. 2719,
    1022–1037.'
  mla: De Alfaro, Luca, et al. “Discounting the Future in Systems Theory.” <i>Proceedings
    of the 30th International Colloquium on Automata, Languages and Programming</i>,
    vol. 2719, Springer, 2003, pp. 1022–37, doi:<a href="https://doi.org/10.1007/3-540-45061-0_79">10.1007/3-540-45061-0_79</a>.
  short: L. De Alfaro, T.A. Henzinger, R. Majumdar, in:, Proceedings of the 30th International
    Colloquium on Automata, Languages and Programming, Springer, 2003, pp. 1022–1037.
conference:
  end_date: 2003-07-04
  location: Eindhoven, The Netherlands
  name: 'ICALP: Automata, Languages and Programming'
  start_date: 2003-06-30
date_created: 2018-12-11T12:09:50Z
date_published: 2003-06-25T00:00:00Z
date_updated: 2023-07-26T13:07:31Z
day: '25'
doi: 10.1007/3-540-45061-0_79
extern: '1'
intvolume: '      2719'
language:
- iso: eng
month: '06'
oa_version: None
page: 1022 - 1037
publication: Proceedings of the 30th International Colloquium on Automata, Languages
  and Programming
publication_identifier:
  isbn:
  - '9783540404934'
publication_status: published
publisher: Springer
publist_id: '77'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discounting the future in systems theory
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2719
year: '2003'
...