---
_id: '1227'
abstract:
- lang: eng
  text: Many biological systems can be modeled as multiaffine hybrid systems. Due
    to the nonlinearity of multiaffine systems, it is difficult to verify their properties
    of interest directly. A common strategy to tackle this problem is to construct
    and analyze a discrete overapproximation of the original system. However, the
    conservativeness of a discrete abstraction significantly determines the level
    of confidence we can have in the properties of the original system. In this paper,
    in order to reduce the conservativeness of a discrete abstraction, we propose
    a new method based on a sufficient and necessary decision condition for computing
    discrete transitions between states in the abstract system. We assume the state
    space partition of a multiaffine system to be based on a set of multivariate polynomials.
    Hence, a rectangular partition defined in terms of polynomials of the form (xi
    − c) is just a simple case of multivariate polynomial partition, and the new decision
    condition applies naturally. We analyze and demonstrate the improvement of our
    method over the existing methods using some examples.
acknowledgement: This research was supported in part by the Austrian Science Fund
  (FWF) under grants S11402-N23, S11405-N23 and S11412-N23 (RiSE/SHiNE) and Z211-N23
  (Wittgenstein Award).
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Hui
  full_name: Kong, Hui
  id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87
  last_name: Kong
  orcid: 0000-0002-3066-6941
- first_name: Ezio
  full_name: Bartocci, Ezio
  last_name: Bartocci
- first_name: Sergiy
  full_name: Bogomolov, Sergiy
  id: 369D9A44-F248-11E8-B48F-1D18A9856A87
  last_name: Bogomolov
  orcid: 0000-0002-0686-0365
- first_name: Radu
  full_name: Grosu, Radu
  last_name: Grosu
- 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: Yu
  full_name: Jiang, Yu
  last_name: Jiang
- first_name: Christian
  full_name: Schilling, Christian
  id: 3A2F4DCE-F248-11E8-B48F-1D18A9856A87
  last_name: Schilling
  orcid: 0000-0003-3658-1065
citation:
  ama: 'Kong H, Bartocci E, Bogomolov S, et al. Discrete abstraction of multiaffine
    systems. In: Vol 9957. Springer; 2016:128-144. doi:<a href="https://doi.org/10.1007/978-3-319-47151-8_9">10.1007/978-3-319-47151-8_9</a>'
  apa: 'Kong, H., Bartocci, E., Bogomolov, S., Grosu, R., Henzinger, T. A., Jiang,
    Y., &#38; Schilling, C. (2016). Discrete abstraction of multiaffine systems (Vol.
    9957, pp. 128–144). Presented at the HSB: Hybrid Systems Biology, Grenoble, France:
    Springer. <a href="https://doi.org/10.1007/978-3-319-47151-8_9">https://doi.org/10.1007/978-3-319-47151-8_9</a>'
  chicago: Kong, Hui, Ezio Bartocci, Sergiy Bogomolov, Radu Grosu, Thomas A Henzinger,
    Yu Jiang, and Christian Schilling. “Discrete Abstraction of Multiaffine Systems,”
    9957:128–44. Springer, 2016. <a href="https://doi.org/10.1007/978-3-319-47151-8_9">https://doi.org/10.1007/978-3-319-47151-8_9</a>.
  ieee: 'H. Kong <i>et al.</i>, “Discrete abstraction of multiaffine systems,” presented
    at the HSB: Hybrid Systems Biology, Grenoble, France, 2016, vol. 9957, pp. 128–144.'
  ista: 'Kong H, Bartocci E, Bogomolov S, Grosu R, Henzinger TA, Jiang Y, Schilling
    C. 2016. Discrete abstraction of multiaffine systems. HSB: Hybrid Systems Biology,
    LNCS, vol. 9957, 128–144.'
  mla: Kong, Hui, et al. <i>Discrete Abstraction of Multiaffine Systems</i>. Vol.
    9957, Springer, 2016, pp. 128–44, doi:<a href="https://doi.org/10.1007/978-3-319-47151-8_9">10.1007/978-3-319-47151-8_9</a>.
  short: H. Kong, E. Bartocci, S. Bogomolov, R. Grosu, T.A. Henzinger, Y. Jiang, C.
    Schilling, in:, Springer, 2016, pp. 128–144.
conference:
  end_date: 2016-10-21
  location: Grenoble, France
  name: 'HSB: Hybrid Systems Biology'
  start_date: 2016-10-20
date_created: 2018-12-11T11:50:49Z
date_published: 2016-09-25T00:00:00Z
date_updated: 2025-09-22T09:24:50Z
day: '25'
ddc:
- '005'
department:
- _id: ToHe
doi: 10.1007/978-3-319-47151-8_9
external_id:
  isi:
  - '000389928100009'
file:
- access_level: open_access
  checksum: 994e164b558c47bacf8dc066dd27c8fc
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:10:49Z
  date_updated: 2020-07-14T12:44:39Z
  file_id: '4840'
  file_name: IST-2017-781-v1+1_main.pdf
  file_size: 683955
  relation: main_file
file_date_updated: 2020-07-14T12:44:39Z
has_accepted_license: '1'
intvolume: '      9957'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 128 - 144
project:
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z211
  name: Formal methods for the design and analysis of complex systems
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: S 11407_N23
  name: Rigorous Systems Engineering
publication_status: published
publisher: Springer
publist_id: '6107'
pubrep_id: '781'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete abstraction of multiaffine systems
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 9957
year: '2016'
...