---
_id: '12467'
abstract:
- lang: eng
text: Safety and liveness are elementary concepts of computation, and the foundation
of many verification paradigms. The safety-liveness classification of boolean
properties characterizes whether a given property can be falsified by observing
a finite prefix of an infinite computation trace (always for safety, never for
liveness). In quantitative specification and verification, properties assign not
truth values, but quantitative values to infinite traces (e.g., a cost, or the
distance to a boolean property). We introduce quantitative safety and liveness,
and we prove that our definitions induce conservative quantitative generalizations
of both (1)~the safety-progress hierarchy of boolean properties and (2)~the safety-liveness
decomposition of boolean properties. In particular, we show that every quantitative
property can be written as the pointwise minimum of a quantitative safety property
and a quantitative liveness property. Consequently, like boolean properties, also
quantitative properties can be min-decomposed into safety and liveness parts,
or alternatively, max-decomposed into co-safety and co-liveness parts. Moreover,
quantitative properties can be approximated naturally. We prove that every quantitative
property that has both safe and co-safe approximations can be monitored arbitrarily
precisely by a monitor that uses only a finite number of states.
acknowledgement: We thank the anonymous reviewers for their helpful comments. This
work was supported in part by the ERC-2020-AdG 101020093.
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- 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: Nicolas Adrien
full_name: Mazzocchi, Nicolas Adrien
id: b26baa86-3308-11ec-87b0-8990f34baa85
last_name: Mazzocchi
- first_name: Naci E
full_name: Sarac, Naci E
id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425
last_name: Sarac
citation:
ama: 'Henzinger TA, Mazzocchi NA, Sarac NE. Quantitative safety and liveness. In:
26th International Conference Foundations of Software Science and Computation
Structures. Vol 13992. Springer Nature; 2023:349-370. doi:10.1007/978-3-031-30829-1_17'
apa: 'Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2023). Quantitative
safety and liveness. In 26th International Conference Foundations of Software
Science and Computation Structures (Vol. 13992, pp. 349–370). Paris, France:
Springer Nature. https://doi.org/10.1007/978-3-031-30829-1_17'
chicago: Henzinger, Thomas A, Nicolas Adrien Mazzocchi, and Naci E Sarac. “Quantitative
Safety and Liveness.” In 26th International Conference Foundations of Software
Science and Computation Structures, 13992:349–70. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-30829-1_17.
ieee: T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “Quantitative safety and
liveness,” in 26th International Conference Foundations of Software Science
and Computation Structures, Paris, France, 2023, vol. 13992, pp. 349–370.
ista: 'Henzinger TA, Mazzocchi NA, Sarac NE. 2023. Quantitative safety and liveness.
26th International Conference Foundations of Software Science and Computation
Structures. FOSSACS: Foundations of Software Science and Computation Structures,
LNCS, vol. 13992, 349–370.'
mla: Henzinger, Thomas A., et al. “Quantitative Safety and Liveness.” 26th International
Conference Foundations of Software Science and Computation Structures, vol.
13992, Springer Nature, 2023, pp. 349–70, doi:10.1007/978-3-031-30829-1_17.
short: T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 26th International Conference
Foundations of Software Science and Computation Structures, Springer Nature, 2023,
pp. 349–370.
conference:
end_date: 2023-04-27
location: Paris, France
name: 'FOSSACS: Foundations of Software Science and Computation Structures'
start_date: 2023-04-22
date_created: 2023-01-31T07:23:56Z
date_published: 2023-04-21T00:00:00Z
date_updated: 2023-07-14T11:20:27Z
day: '21'
ddc:
- '000'
department:
- _id: GradSch
- _id: ToHe
doi: 10.1007/978-3-031-30829-1_17
ec_funded: 1
external_id:
arxiv:
- '2301.11175'
file:
- access_level: open_access
checksum: 981025aed580b6b27c426cb8856cf63e
content_type: application/pdf
creator: esarac
date_created: 2023-01-31T07:22:21Z
date_updated: 2023-01-31T07:22:21Z
file_id: '12468'
file_name: qsl.pdf
file_size: 449027
relation: main_file
success: 1
- access_level: open_access
checksum: f16e2af1e0eb243158ab0f0fe74e7d5a
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T10:28:09Z
date_updated: 2023-06-19T10:28:09Z
file_id: '13153'
file_name: 2023_LNCS_HenzingerT.pdf
file_size: 1048171
relation: main_file
success: 1
file_date_updated: 2023-06-19T10:28:09Z
has_accepted_license: '1'
intvolume: ' 13992'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 349-370
project:
- _id: 62781420-2b32-11ec-9570-8d9b63373d4d
call_identifier: H2020
grant_number: '101020093'
name: Vigilant Algorithmic Monitoring of Software
publication: 26th International Conference Foundations of Software Science and Computation
Structures
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031308284'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative safety and liveness
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 13992
year: '2023'
...