---
_id: '1389'
abstract:
- lang: eng
  text: "The continuous evolution of a wide variety of systems, including continous-time
    Markov chains and linear hybrid automata, can be\r\ndescribed in terms of linear
    differential equations. In this paper we study the decision problem of whether
    the solution x(t) of a system of linear differential equations dx/dt = Ax reaches
    a target halfspace infinitely often. This recurrent reachability problem can\r\nequivalently
    be formulated as the following Infinite Zeros Problem: does a real-valued function
    f:R≥0 --> R satisfying a given linear\r\ndifferential equation have infinitely
    many zeros? Our main decidability result is that if the differential equation
    has order at most 7, then the Infinite Zeros Problem is decidable. On the other
    hand, we show that a decision procedure for the Infinite Zeros Problem at order
    9 (and above) would entail a major breakthrough in Diophantine Approximation,
    specifically an algorithm for computing the Lagrange constants of arbitrary real
    algebraic numbers to arbitrary precision."
article_processing_charge: No
arxiv: 1
author:
- first_name: Ventsislav K
  full_name: Chonev, Ventsislav K
  id: 36CBE2E6-F248-11E8-B48F-1D18A9856A87
  last_name: Chonev
- first_name: Joël
  full_name: Ouaknine, Joël
  last_name: Ouaknine
- first_name: James
  full_name: Worrell, James
  last_name: Worrell
citation:
  ama: 'Chonev VK, Ouaknine J, Worrell J. On recurrent reachability for continuous
    linear dynamical systems. In: <i>LICS ’16</i>. IEEE; 2016:515-524. doi:<a href="https://doi.org/10.1145/2933575.2934548">10.1145/2933575.2934548</a>'
  apa: 'Chonev, V. K., Ouaknine, J., &#38; Worrell, J. (2016). On recurrent reachability
    for continuous linear dynamical systems. In <i>LICS ’16</i> (pp. 515–524). New
    York, NY, USA: IEEE. <a href="https://doi.org/10.1145/2933575.2934548">https://doi.org/10.1145/2933575.2934548</a>'
  chicago: Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On Recurrent Reachability
    for Continuous Linear Dynamical Systems.” In <i>LICS ’16</i>, 515–24. IEEE, 2016.
    <a href="https://doi.org/10.1145/2933575.2934548">https://doi.org/10.1145/2933575.2934548</a>.
  ieee: V. K. Chonev, J. Ouaknine, and J. Worrell, “On recurrent reachability for
    continuous linear dynamical systems,” in <i>LICS ’16</i>, New York, NY, USA, 2016,
    pp. 515–524.
  ista: 'Chonev VK, Ouaknine J, Worrell J. 2016. On recurrent reachability for continuous
    linear dynamical systems. LICS ’16. LICS: Logic in Computer Science, 515–524.'
  mla: Chonev, Ventsislav K., et al. “On Recurrent Reachability for Continuous Linear
    Dynamical Systems.” <i>LICS ’16</i>, IEEE, 2016, pp. 515–24, doi:<a href="https://doi.org/10.1145/2933575.2934548">10.1145/2933575.2934548</a>.
  short: V.K. Chonev, J. Ouaknine, J. Worrell, in:, LICS ’16, IEEE, 2016, pp. 515–524.
conference:
  end_date: 2018-07-08
  location: New York, NY, USA
  name: 'LICS: Logic in Computer Science'
  start_date: 2018-07-05
date_created: 2018-12-11T11:51:44Z
date_published: 2016-07-05T00:00:00Z
date_updated: 2025-09-22T07:31:08Z
day: '05'
department:
- _id: KrCh
doi: 10.1145/2933575.2934548
ec_funded: 1
external_id:
  arxiv:
  - '1507.03632'
  isi:
  - '000387609200052'
fulldoi: https://doi.org/10.1145/2933575.2934548
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1507.03632
month: '07'
oa: 1
oa_version: Preprint
page: 515 - 524
project:
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '279307'
  name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S 11407_N23
  name: Rigorous Systems Engineering
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '267989'
  name: Quantitative Reactive Modeling
publication: LICS '16
publication_status: published
publisher: IEEE
publist_id: '5820'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On recurrent reachability for continuous linear dynamical systems
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2016'
...