---
_id: '7808'
abstract:
- lang: eng
text: Quantization converts neural networks into low-bit fixed-point computations
which can be carried out by efficient integer-only hardware, and is standard practice
for the deployment of neural networks on real-time embedded devices. However,
like their real-numbered counterpart, quantized networks are not immune to malicious
misclassification caused by adversarial attacks. We investigate how quantization
affects a network’s robustness to adversarial attacks, which is a formal verification
question. We show that neither robustness nor non-robustness are monotonic with
changing the number of bits for the representation and, also, neither are preserved
by quantization from a real-numbered network. For this reason, we introduce a
verification method for quantized neural networks which, using SMT solving over
bit-vectors, accounts for their exact, bit-precise semantics. We built a tool
and analyzed the effect of quantization on a classifier for the MNIST dataset.
We demonstrate that, compared to our method, existing methods for the analysis
of real-numbered networks often derive false conclusions about their quantizations,
both when determining robustness and when detecting attacks, and that existing
methods for quantized networks often miss attacks. Furthermore, we applied our
method beyond robustness, showing how the number of bits in quantization enlarges
the gender bias of a predictor for students’ grades.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- 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: Mathias
full_name: Lechner, Mathias
id: 3DC22916-F248-11E8-B48F-1D18A9856A87
last_name: Lechner
citation:
ama: 'Giacobbe M, Henzinger TA, Lechner M. How many bits does it take to quantize
your neural network? In: International Conference on Tools and Algorithms for
the Construction and Analysis of Systems. Vol 12079. Springer Nature; 2020:79-97.
doi:10.1007/978-3-030-45237-7_5'
apa: 'Giacobbe, M., Henzinger, T. A., & Lechner, M. (2020). How many bits does
it take to quantize your neural network? In International Conference on Tools
and Algorithms for the Construction and Analysis of Systems (Vol. 12079, pp.
79–97). Dublin, Ireland: Springer Nature. https://doi.org/10.1007/978-3-030-45237-7_5'
chicago: Giacobbe, Mirco, Thomas A Henzinger, and Mathias Lechner. “How Many Bits
Does It Take to Quantize Your Neural Network?” In International Conference
on Tools and Algorithms for the Construction and Analysis of Systems, 12079:79–97.
Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45237-7_5.
ieee: M. Giacobbe, T. A. Henzinger, and M. Lechner, “How many bits does it take
to quantize your neural network?,” in International Conference on Tools and
Algorithms for the Construction and Analysis of Systems, Dublin, Ireland,
2020, vol. 12079, pp. 79–97.
ista: 'Giacobbe M, Henzinger TA, Lechner M. 2020. How many bits does it take to
quantize your neural network? International Conference on Tools and Algorithms
for the Construction and Analysis of Systems. TACAS: Tools and Algorithms for
the Construction and Analysis of Systems, LNCS, vol. 12079, 79–97.'
mla: Giacobbe, Mirco, et al. “How Many Bits Does It Take to Quantize Your Neural
Network?” International Conference on Tools and Algorithms for the Construction
and Analysis of Systems, vol. 12079, Springer Nature, 2020, pp. 79–97, doi:10.1007/978-3-030-45237-7_5.
short: M. Giacobbe, T.A. Henzinger, M. Lechner, in:, International Conference on
Tools and Algorithms for the Construction and Analysis of Systems, Springer Nature,
2020, pp. 79–97.
conference:
end_date: 2020-04-30
location: Dublin, Ireland
name: 'TACAS: Tools and Algorithms for the Construction and Analysis of Systems'
start_date: 2020-04-25
date_created: 2020-05-10T22:00:49Z
date_published: 2020-04-17T00:00:00Z
date_updated: 2023-06-23T07:01:11Z
day: '17'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-030-45237-7_5
file:
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checksum: f19905a42891fe5ce93d69143fa3f6fb
content_type: application/pdf
creator: dernst
date_created: 2020-05-26T12:48:15Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7893'
file_name: 2020_TACAS_Giacobbe.pdf
file_size: 2744030
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 12079'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 79-97
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: International Conference on Tools and Algorithms for the Construction
and Analysis of Systems
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030452360'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11362'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: How many bits does it take to quantize your neural network?
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12079
year: '2020'
...
---
_id: '10877'
abstract:
- lang: eng
text: 'This report presents the results of a friendly competition for formal verification
of continuous and hybrid systems with piecewise constant dynamics. The friendly
competition took place as part of the workshop Applied Verification for Continuous
and Hybrid Systems (ARCH) in 2019. In this third edition, six tools have been
applied to solve five different benchmark problems in the category for piecewise
constant dynamics: BACH, Lyse, Hy- COMP, PHAVer/SX, PHAVerLite, and VeriSiMPL.
Compared to last year, a new tool has participated (HyCOMP) and PHAVerLite has
replaced PHAVer-lite. The result is a snap- shot of the current landscape of tools
and the types of benchmarks they are particularly suited for. Due to the diversity
of problems, we are not ranking tools, yet the presented results probably provide
the most complete assessment of tools for the safety verification of continuous
and hybrid systems with piecewise constant dynamics up to this date.'
acknowledgement: "The authors gratefully acknowledge \fnancial support by the European
Commission project\r\nUnCoVerCPS under grant number 643921. Lei Bu is supported
by the National Natural Science\r\nFoundation of China (No.61572249)."
alternative_title:
- EPiC Series in Computing
article_processing_charge: No
author:
- first_name: Goran
full_name: Frehse, Goran
last_name: Frehse
- first_name: Alessandro
full_name: Abate, Alessandro
last_name: Abate
- first_name: Dieky
full_name: Adzkiya, Dieky
last_name: Adzkiya
- first_name: Anna
full_name: Becchi, Anna
last_name: Becchi
- first_name: Lei
full_name: Bu, Lei
last_name: Bu
- first_name: Alessandro
full_name: Cimatti, Alessandro
last_name: Cimatti
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Alberto
full_name: Griggio, Alberto
last_name: Griggio
- first_name: Sergio
full_name: Mover, Sergio
last_name: Mover
- first_name: Muhammad Syifa'ul
full_name: Mufid, Muhammad Syifa'ul
last_name: Mufid
- first_name: Idriss
full_name: Riouak, Idriss
last_name: Riouak
- first_name: Stefano
full_name: Tonetta, Stefano
last_name: Tonetta
- first_name: Enea
full_name: Zaffanella, Enea
last_name: Zaffanella
citation:
ama: 'Frehse G, Abate A, Adzkiya D, et al. ARCH-COMP19 Category Report: Hybrid systems
with piecewise constant dynamics. In: Frehse G, Althoff M, eds. ARCH19. 6th
International Workshop on Applied Verification of Continuous and Hybrid Systems.
Vol 61. EasyChair; 2019:1-13. doi:10.29007/rjwn'
apa: 'Frehse, G., Abate, A., Adzkiya, D., Becchi, A., Bu, L., Cimatti, A., … Zaffanella,
E. (2019). ARCH-COMP19 Category Report: Hybrid systems with piecewise constant
dynamics. In G. Frehse & M. Althoff (Eds.), ARCH19. 6th International Workshop
on Applied Verification of Continuous and Hybrid Systems (Vol. 61, pp. 1–13).
Montreal, Canada: EasyChair. https://doi.org/10.29007/rjwn'
chicago: 'Frehse, Goran, Alessandro Abate, Dieky Adzkiya, Anna Becchi, Lei Bu, Alessandro
Cimatti, Mirco Giacobbe, et al. “ARCH-COMP19 Category Report: Hybrid Systems with
Piecewise Constant Dynamics.” In ARCH19. 6th International Workshop on Applied
Verification of Continuous and Hybrid Systems, edited by Goran Frehse and
Matthias Althoff, 61:1–13. EasyChair, 2019. https://doi.org/10.29007/rjwn.'
ieee: 'G. Frehse et al., “ARCH-COMP19 Category Report: Hybrid systems with
piecewise constant dynamics,” in ARCH19. 6th International Workshop on Applied
Verification of Continuous and Hybrid Systems, Montreal, Canada, 2019, vol.
61, pp. 1–13.'
ista: 'Frehse G, Abate A, Adzkiya D, Becchi A, Bu L, Cimatti A, Giacobbe M, Griggio
A, Mover S, Mufid MS, Riouak I, Tonetta S, Zaffanella E. 2019. ARCH-COMP19 Category
Report: Hybrid systems with piecewise constant dynamics. ARCH19. 6th International
Workshop on Applied Verification of Continuous and Hybrid Systems. ARCH: International
Workshop on Applied Verification on Continuous and Hybrid Systems, EPiC Series
in Computing, vol. 61, 1–13.'
mla: 'Frehse, Goran, et al. “ARCH-COMP19 Category Report: Hybrid Systems with Piecewise
Constant Dynamics.” ARCH19. 6th International Workshop on Applied Verification
of Continuous and Hybrid Systems, edited by Goran Frehse and Matthias Althoff,
vol. 61, EasyChair, 2019, pp. 1–13, doi:10.29007/rjwn.'
short: G. Frehse, A. Abate, D. Adzkiya, A. Becchi, L. Bu, A. Cimatti, M. Giacobbe,
A. Griggio, S. Mover, M.S. Mufid, I. Riouak, S. Tonetta, E. Zaffanella, in:, G.
Frehse, M. Althoff (Eds.), ARCH19. 6th International Workshop on Applied Verification
of Continuous and Hybrid Systems, EasyChair, 2019, pp. 1–13.
conference:
end_date: 2019-04-15
location: Montreal, Canada
name: 'ARCH: International Workshop on Applied Verification on Continuous and Hybrid
Systems'
start_date: 2019-04-15
date_created: 2022-03-18T12:29:23Z
date_published: 2019-05-25T00:00:00Z
date_updated: 2022-05-17T07:09:47Z
day: '25'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.29007/rjwn
editor:
- first_name: Goran
full_name: Frehse, Goran
last_name: Frehse
- first_name: Matthias
full_name: Althoff, Matthias
last_name: Althoff
file:
- access_level: open_access
checksum: 4b92e333db7b4e2349501a804dfede69
content_type: application/pdf
creator: dernst
date_created: 2022-05-17T06:55:49Z
date_updated: 2022-05-17T06:55:49Z
file_id: '11391'
file_name: 2019_EPiCs_Frehse.pdf
file_size: 346415
relation: main_file
success: 1
file_date_updated: 2022-05-17T06:55:49Z
has_accepted_license: '1'
intvolume: ' 61'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1-13
publication: ARCH19. 6th International Workshop on Applied Verification of Continuous
and Hybrid Systems
publication_identifier:
issn:
- 2398-7340
publication_status: published
publisher: EasyChair
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'ARCH-COMP19 Category Report: Hybrid systems with piecewise constant dynamics'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2019'
...
---
_id: '6894'
abstract:
- lang: eng
text: "Hybrid automata combine finite automata and dynamical systems, and model
the interaction of digital with physical systems. Formal analysis that can guarantee
the safety of all behaviors or rigorously witness failures, while unsolvable in
general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking,
assisted theorem proving.\r\nNevertheless, very few methods have addressed the
time-unbounded reachability analysis of hybrid automata and, for current sound
and automatic tools, scalability remains critical. We develop methods for the
polyhedral abstraction of hybrid automata, which construct coarse overapproximations
and tightens them incrementally, in a CEGAR fashion. We use template polyhedra,
i.e., polyhedra whose facets are normal to a given set of directions.\r\nWhile,
previously, directions were given by the user, we introduce (1) the first method\r\nfor
computing template directions from spurious counterexamples, so as to generalize
and\r\neliminate them. The method applies naturally to convex hybrid automata,
i.e., hybrid\r\nautomata with (possibly non-linear) convex constraints on derivatives
only, while for linear\r\nODE requires further abstraction. Specifically, we introduce
(2) the conic abstractions,\r\nwhich, partitioning the state space into appropriate
(possibly non-uniform) cones, divide\r\ncurvy trajectories into relatively straight
sections, suitable for polyhedral abstractions.\r\nFinally, we introduce (3) space-time
interpolation, which, combining interval arithmetic\r\nand template refinement,
computes appropriate (possibly non-uniform) time partitioning\r\nand template
directions along spurious trajectories, so as to eliminate them.\r\nWe obtain
sound and automatic methods for the reachability analysis over dense\r\nand unbounded
time of convex hybrid automata and hybrid automata with linear ODE.\r\nWe build
prototype tools and compare—favorably—our methods against the respective\r\nstate-of-the-art
tools, on several benchmarks."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
citation:
ama: Giacobbe M. Automatic time-unbounded reachability analysis of hybrid systems.
2019. doi:10.15479/AT:ISTA:6894
apa: Giacobbe, M. (2019). Automatic time-unbounded reachability analysis of hybrid
systems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:6894
chicago: Giacobbe, Mirco. “Automatic Time-Unbounded Reachability Analysis of Hybrid
Systems.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:6894.
ieee: M. Giacobbe, “Automatic time-unbounded reachability analysis of hybrid systems,”
Institute of Science and Technology Austria, 2019.
ista: Giacobbe M. 2019. Automatic time-unbounded reachability analysis of hybrid
systems. Institute of Science and Technology Austria.
mla: Giacobbe, Mirco. Automatic Time-Unbounded Reachability Analysis of Hybrid
Systems. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:6894.
short: M. Giacobbe, Automatic Time-Unbounded Reachability Analysis of Hybrid Systems,
Institute of Science and Technology Austria, 2019.
date_created: 2019-09-22T14:08:44Z
date_published: 2019-09-30T00:00:00Z
date_updated: 2023-09-19T09:30:43Z
day: '30'
ddc:
- '000'
degree_awarded: PhD
department:
- _id: ToHe
doi: 10.15479/AT:ISTA:6894
file:
- access_level: open_access
checksum: 773beaf4a85dc2acc2c12b578fbe1965
content_type: application/pdf
creator: mgiacobbe
date_created: 2019-09-27T14:15:05Z
date_updated: 2020-07-14T12:47:43Z
file_id: '6916'
file_name: giacobbe_thesis.pdf
file_size: 4100685
relation: main_file
- access_level: closed
checksum: 97f1c3da71feefd27e6e625d32b4c75b
content_type: application/gzip
creator: mgiacobbe
date_created: 2019-09-27T14:22:04Z
date_updated: 2020-07-14T12:47:43Z
file_id: '6917'
file_name: giacobbe_thesis_src.tar.gz
file_size: 7959732
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file_date_updated: 2020-07-14T12:47:43Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '132'
publication_identifier:
eissn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '631'
relation: part_of_dissertation
status: public
- id: '647'
relation: part_of_dissertation
status: public
- id: '140'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
title: Automatic time-unbounded reachability analysis of hybrid systems
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: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...
---
_id: '7453'
abstract:
- lang: eng
text: We illustrate the ingredients of the state-of-the-art of model-based approach
for the formal design and verification of cyber-physical systems. To capture the
interaction between a discrete controller and its continuously evolving environment,
we use the formal models of timed and hybrid automata. We explain the steps of
modeling and verification in the tools Uppaal and SpaceEx using a case study based
on a dual-chamber implantable pacemaker monitoring a human heart. We show how
to design a model as a composition of components, how to construct models at varying
levels of detail, how to establish that one model is an abstraction of another,
how to specify correctness requirements using temporal logic, and how to verify
that a model satisfies a logical requirement.
acknowledgement: This research was supported in part by the Austrian Science Fund
(FWF) under grants S11402-N23(RiSE/SHiNE) and Z211-N23 (Wittgenstein Award). This
research has received funding from the Sino-Danish Basic Research Centre, IDEA4CPS,
funded by the Danish National Research Foundation and the National Science Foundation,
China, the Innovation Fund Denmark centre DiCyPS, as well as the ERC Advanced Grant
LASSO.
alternative_title:
- Lecture Notes in Computer Science
article_processing_charge: No
author:
- first_name: Rajeev
full_name: Alur, Rajeev
last_name: Alur
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- 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: Kim G.
full_name: Larsen, Kim G.
last_name: Larsen
- first_name: Marius
full_name: Mikučionis, Marius
last_name: Mikučionis
citation:
ama: 'Alur R, Giacobbe M, Henzinger TA, Larsen KG, Mikučionis M. Continuous-time
models for system design and analysis. In: Steffen B, Woeginger G, eds. Computing
and Software Science. Vol 10000. LNCS. Springer Nature; 2019:452-477. doi:10.1007/978-3-319-91908-9_22'
apa: Alur, R., Giacobbe, M., Henzinger, T. A., Larsen, K. G., & Mikučionis,
M. (2019). Continuous-time models for system design and analysis. In B. Steffen
& G. Woeginger (Eds.), Computing and Software Science (Vol. 10000,
pp. 452–477). Springer Nature. https://doi.org/10.1007/978-3-319-91908-9_22
chicago: Alur, Rajeev, Mirco Giacobbe, Thomas A Henzinger, Kim G. Larsen, and Marius
Mikučionis. “Continuous-Time Models for System Design and Analysis.” In Computing
and Software Science, edited by Bernhard Steffen and Gerhard Woeginger, 10000:452–77.
LNCS. Springer Nature, 2019. https://doi.org/10.1007/978-3-319-91908-9_22.
ieee: R. Alur, M. Giacobbe, T. A. Henzinger, K. G. Larsen, and M. Mikučionis, “Continuous-time
models for system design and analysis,” in Computing and Software Science,
vol. 10000, B. Steffen and G. Woeginger, Eds. Springer Nature, 2019, pp. 452–477.
ista: 'Alur R, Giacobbe M, Henzinger TA, Larsen KG, Mikučionis M. 2019.Continuous-time
models for system design and analysis. In: Computing and Software Science. Lecture
Notes in Computer Science, vol. 10000, 452–477.'
mla: Alur, Rajeev, et al. “Continuous-Time Models for System Design and Analysis.”
Computing and Software Science, edited by Bernhard Steffen and Gerhard
Woeginger, vol. 10000, Springer Nature, 2019, pp. 452–77, doi:10.1007/978-3-319-91908-9_22.
short: R. Alur, M. Giacobbe, T.A. Henzinger, K.G. Larsen, M. Mikučionis, in:, B.
Steffen, G. Woeginger (Eds.), Computing and Software Science, Springer Nature,
2019, pp. 452–477.
date_created: 2020-02-05T10:51:44Z
date_published: 2019-10-05T00:00:00Z
date_updated: 2022-09-06T08:25:52Z
day: '05'
department:
- _id: ToHe
doi: 10.1007/978-3-319-91908-9_22
editor:
- first_name: Bernhard
full_name: Steffen, Bernhard
last_name: Steffen
- first_name: Gerhard
full_name: Woeginger, Gerhard
last_name: Woeginger
intvolume: ' 10000'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/978-3-319-91908-9_22
month: '10'
oa: 1
oa_version: Published Version
page: 452-477
project:
- _id: 25F2ACDE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: Computing and Software Science
publication_identifier:
eisbn:
- '9783319919089'
eissn:
- 0302-9743
isbn:
- '9783319919072'
issn:
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: LNCS
status: public
title: Continuous-time models for system design and analysis
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10000
year: '2019'
...
---
_id: '140'
abstract:
- lang: eng
text: Reachability analysis is difficult for hybrid automata with affine differential
equations, because the reach set needs to be approximated. Promising abstraction
techniques usually employ interval methods or template polyhedra. Interval methods
account for dense time and guarantee soundness, and there are interval-based tools
that overapproximate affine flowpipes. But interval methods impose bounded and
rigid shapes, which make refinement expensive and fixpoint detection difficult.
Template polyhedra, on the other hand, can be adapted flexibly and can be unbounded,
but sound template refinement for unbounded reachability analysis has been implemented
only for systems with piecewise constant dynamics. We capitalize on the advantages
of both techniques, combining interval arithmetic and template polyhedra, using
the former to abstract time and the latter to abstract space. During a CEGAR loop,
whenever a spurious error trajectory is found, we compute additional space constraints
and split time intervals, and use these space-time interpolants to eliminate the
counterexample. Space-time interpolation offers a lazy, flexible framework for
increasing precision while guaranteeing soundness, both for error avoidance and
fixpoint detection. To the best of out knowledge, this is the first abstraction
refinement scheme for the reachability analysis over unbounded and dense time
of affine hybrid systems, which is both sound and automatic. We demonstrate the
effectiveness of our algorithm with several benchmark examples, which cannot be
handled by other tools.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Goran
full_name: Frehse, Goran
last_name: Frehse
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Frehse G, Giacobbe M, Henzinger TA. Space-time interpolants. In: Vol 10981.
Springer; 2018:468-486. doi:10.1007/978-3-319-96145-3_25'
apa: 'Frehse, G., Giacobbe, M., & Henzinger, T. A. (2018). Space-time interpolants
(Vol. 10981, pp. 468–486). Presented at the CAV: Computer Aided Verification,
Oxford, United Kingdom: Springer. https://doi.org/10.1007/978-3-319-96145-3_25'
chicago: Frehse, Goran, Mirco Giacobbe, and Thomas A Henzinger. “Space-Time Interpolants,”
10981:468–86. Springer, 2018. https://doi.org/10.1007/978-3-319-96145-3_25.
ieee: 'G. Frehse, M. Giacobbe, and T. A. Henzinger, “Space-time interpolants,” presented
at the CAV: Computer Aided Verification, Oxford, United Kingdom, 2018, vol. 10981,
pp. 468–486.'
ista: 'Frehse G, Giacobbe M, Henzinger TA. 2018. Space-time interpolants. CAV: Computer
Aided Verification, LNCS, vol. 10981, 468–486.'
mla: Frehse, Goran, et al. Space-Time Interpolants. Vol. 10981, Springer,
2018, pp. 468–86, doi:10.1007/978-3-319-96145-3_25.
short: G. Frehse, M. Giacobbe, T.A. Henzinger, in:, Springer, 2018, pp. 468–486.
conference:
end_date: 2018-07-17
location: Oxford, United Kingdom
name: 'CAV: Computer Aided Verification'
start_date: 2018-07-14
date_created: 2018-12-11T11:44:50Z
date_published: 2018-07-18T00:00:00Z
date_updated: 2023-09-19T09:30:43Z
day: '18'
ddc:
- '005'
department:
- _id: ToHe
doi: 10.1007/978-3-319-96145-3_25
external_id:
isi:
- '000491481600025'
file:
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creator: system
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date_updated: 2020-07-14T12:44:50Z
file_id: '5310'
file_name: IST-2018-1010-v1+1_space-time_interpolants.pdf
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relation: main_file
file_date_updated: 2020-07-14T12:44:50Z
has_accepted_license: '1'
intvolume: ' 10981'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 468 - 486
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F5A88A-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Moderne Concurrency Paradigms
publication_identifier:
issn:
- '03029743'
publication_status: published
publisher: Springer
publist_id: '7783'
pubrep_id: '1010'
quality_controlled: '1'
related_material:
record:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Space-time interpolants
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10981
year: '2018'
...
---
_id: '631'
abstract:
- lang: eng
text: Template polyhedra generalize intervals and octagons to polyhedra whose facets
are orthogonal to a given set of arbitrary directions. They have been employed
in the abstract interpretation of programs and, with particular success, in the
reachability analysis of hybrid automata. While previously, the choice of directions
has been left to the user or a heuristic, we present a method for the automatic
discovery of directions that generalize and eliminate spurious counterexamples.
We show that for the class of convex hybrid automata, i.e., hybrid automata with
(possibly nonlinear) convex constraints on derivatives, such directions always
exist and can be found using convex optimization. We embed our method inside a
CEGAR loop, thus enabling the time-unbounded reachability analysis of an important
and richer class of hybrid automata than was previously possible. We evaluate
our method on several benchmarks, demonstrating also its superior efficiency for
the special case of linear hybrid automata.
acknowledgement: This research was supported in part by the Austrian Science Fund
(FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), by
the European Commission under grant 643921 (UnCoVerCPS), and by the ARC project
DP140104219 (Robust AI Planning for Hybrid Systems).
alternative_title:
- LNCS
author:
- first_name: Sergiy
full_name: Bogomolov, Sergiy
id: 369D9A44-F248-11E8-B48F-1D18A9856A87
last_name: Bogomolov
orcid: 0000-0002-0686-0365
- first_name: Goran
full_name: Frehse, Goran
last_name: Frehse
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Bogomolov S, Frehse G, Giacobbe M, Henzinger TA. Counterexample guided refinement
of template polyhedra. In: Vol 10205. Springer; 2017:589-606. doi:10.1007/978-3-662-54577-5_34'
apa: 'Bogomolov, S., Frehse, G., Giacobbe, M., & Henzinger, T. A. (2017). Counterexample
guided refinement of template polyhedra (Vol. 10205, pp. 589–606). Presented at
the TACAS: Tools and Algorithms for the Construction and Analysis of Systems,
Uppsala, Sweden: Springer. https://doi.org/10.1007/978-3-662-54577-5_34'
chicago: Bogomolov, Sergiy, Goran Frehse, Mirco Giacobbe, and Thomas A Henzinger.
“Counterexample Guided Refinement of Template Polyhedra,” 10205:589–606. Springer,
2017. https://doi.org/10.1007/978-3-662-54577-5_34.
ieee: 'S. Bogomolov, G. Frehse, M. Giacobbe, and T. A. Henzinger, “Counterexample
guided refinement of template polyhedra,” presented at the TACAS: Tools and Algorithms
for the Construction and Analysis of Systems, Uppsala, Sweden, 2017, vol. 10205,
pp. 589–606.'
ista: 'Bogomolov S, Frehse G, Giacobbe M, Henzinger TA. 2017. Counterexample guided
refinement of template polyhedra. TACAS: Tools and Algorithms for the Construction
and Analysis of Systems, LNCS, vol. 10205, 589–606.'
mla: Bogomolov, Sergiy, et al. Counterexample Guided Refinement of Template Polyhedra.
Vol. 10205, Springer, 2017, pp. 589–606, doi:10.1007/978-3-662-54577-5_34.
short: S. Bogomolov, G. Frehse, M. Giacobbe, T.A. Henzinger, in:, Springer, 2017,
pp. 589–606.
conference:
end_date: 2017-04-29
location: Uppsala, Sweden
name: 'TACAS: Tools and Algorithms for the Construction and Analysis of Systems'
start_date: 2017-04-22
date_created: 2018-12-11T11:47:36Z
date_published: 2017-03-31T00:00:00Z
date_updated: 2023-09-07T12:53:00Z
day: '31'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-662-54577-5_34
file:
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checksum: f395d0d20102b89aeaad8b4ef4f18f4f
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:41Z
date_updated: 2020-07-14T12:47:27Z
file_id: '4897'
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creator: system
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relation: main_file
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has_accepted_license: '1'
intvolume: ' 10205'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Submitted Version
page: 589 - 606
project:
- _id: 25F5A88A-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Moderne Concurrency Paradigms
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication_identifier:
isbn:
- 978-366254576-8
publication_status: published
publisher: Springer
publist_id: '7162'
pubrep_id: '966'
quality_controlled: '1'
related_material:
record:
- id: '6894'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Counterexample guided refinement of template polyhedra
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10205
year: '2017'
...
---
_id: '647'
abstract:
- lang: eng
text: Despite researchers’ efforts in the last couple of decades, reachability analysis
is still a challenging problem even for linear hybrid systems. Among the existing
approaches, the most practical ones are mainly based on bounded-time reachable
set over-approximations. For the purpose of unbounded-time analysis, one important
strategy is to abstract the original system and find an invariant for the abstraction.
In this paper, we propose an approach to constructing a new kind of abstraction
called conic abstraction for affine hybrid systems, and to computing reachable
sets based on this abstraction. The essential feature of a conic abstraction is
that it partitions the state space of a system into a set of convex polyhedral
cones which is derived from a uniform conic partition of the derivative space.
Such a set of polyhedral cones is able to cut all trajectories of the system into
almost straight segments so that every segment of a reach pipe in a polyhedral
cone tends to be straight as well, and hence can be over-approximated tightly
by polyhedra using similar techniques as HyTech or PHAVer. In particular, for
diagonalizable affine systems, our approach can guarantee to find an invariant
for unbounded reachable sets, which is beyond the capability of bounded-time reachability
analysis tools. We implemented the approach in a tool and experiments on benchmarks
show that our approach is more powerful than SpaceEx and PHAVer in dealing with
diagonalizable systems.
alternative_title:
- LNCS
author:
- first_name: Sergiy
full_name: Bogomolov, Sergiy
id: 369D9A44-F248-11E8-B48F-1D18A9856A87
last_name: Bogomolov
orcid: 0000-0002-0686-0365
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- 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: Hui
full_name: Kong, Hui
id: 3BDE25AA-F248-11E8-B48F-1D18A9856A87
last_name: Kong
orcid: 0000-0002-3066-6941
citation:
ama: 'Bogomolov S, Giacobbe M, Henzinger TA, Kong H. Conic abstractions for hybrid
systems. In: Vol 10419. Springer; 2017:116-132. doi:10.1007/978-3-319-65765-3_7'
apa: 'Bogomolov, S., Giacobbe, M., Henzinger, T. A., & Kong, H. (2017). Conic
abstractions for hybrid systems (Vol. 10419, pp. 116–132). Presented at the FORMATS:
Formal Modelling and Analysis of Timed Systems, Berlin, Germany: Springer. https://doi.org/10.1007/978-3-319-65765-3_7'
chicago: Bogomolov, Sergiy, Mirco Giacobbe, Thomas A Henzinger, and Hui Kong. “Conic
Abstractions for Hybrid Systems,” 10419:116–32. Springer, 2017. https://doi.org/10.1007/978-3-319-65765-3_7.
ieee: 'S. Bogomolov, M. Giacobbe, T. A. Henzinger, and H. Kong, “Conic abstractions
for hybrid systems,” presented at the FORMATS: Formal Modelling and Analysis of
Timed Systems, Berlin, Germany, 2017, vol. 10419, pp. 116–132.'
ista: 'Bogomolov S, Giacobbe M, Henzinger TA, Kong H. 2017. Conic abstractions for
hybrid systems. FORMATS: Formal Modelling and Analysis of Timed Systems, LNCS,
vol. 10419, 116–132.'
mla: Bogomolov, Sergiy, et al. Conic Abstractions for Hybrid Systems. Vol.
10419, Springer, 2017, pp. 116–32, doi:10.1007/978-3-319-65765-3_7.
short: S. Bogomolov, M. Giacobbe, T.A. Henzinger, H. Kong, in:, Springer, 2017,
pp. 116–132.
conference:
end_date: 2017-09-07
location: Berlin, Germany
name: 'FORMATS: Formal Modelling and Analysis of Timed Systems'
start_date: 2017-09-05
date_created: 2018-12-11T11:47:41Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-07T12:53:00Z
day: '01'
ddc:
- '005'
department:
- _id: ToHe
doi: 10.1007/978-3-319-65765-3_7
file:
- access_level: open_access
checksum: faf546914ba29bcf9974ee36b6b16750
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:38Z
date_updated: 2020-07-14T12:47:31Z
file_id: '4956'
file_name: IST-2017-831-v1+1_main.pdf
file_size: 3806864
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file_date_updated: 2020-07-14T12:47:31Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 116 - 132
project:
- _id: 25F5A88A-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Moderne Concurrency Paradigms
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication_identifier:
isbn:
- 978-331965764-6
publication_status: published
publisher: Springer
publist_id: '7129'
pubrep_id: '831'
quality_controlled: '1'
related_material:
record:
- id: '6894'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Conic abstractions for hybrid systems
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: '10419 '
year: '2017'
...
---
_id: '1351'
abstract:
- lang: eng
text: The behaviour of gene regulatory networks (GRNs) is typically analysed using
simulation-based statistical testing-like methods. In this paper, we demonstrate
that we can replace this approach by a formal verification-like method that gives
higher assurance and scalability. We focus on Wagner’s weighted GRN model with
varying weights, which is used in evolutionary biology. In the model, weight parameters
represent the gene interaction strength that may change due to genetic mutations.
For a property of interest, we synthesise the constraints over the parameter space
that represent the set of GRNs satisfying the property. We experimentally show
that our parameter synthesis procedure computes the mutational robustness of GRNs—an
important problem of interest in evolutionary biology—more efficiently than the
classical simulation method. We specify the property in linear temporal logic.
We employ symbolic bounded model checking and SMT solving to compute the space
of GRNs that satisfy the property, which amounts to synthesizing a set of linear
constraints on the weights.
article_processing_charge: No
author:
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Calin C
full_name: Guet, Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
- first_name: Ashutosh
full_name: Gupta, Ashutosh
id: 335E5684-F248-11E8-B48F-1D18A9856A87
last_name: Gupta
- 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: Tiago
full_name: Paixao, Tiago
id: 2C5658E6-F248-11E8-B48F-1D18A9856A87
last_name: Paixao
orcid: 0000-0003-2361-3953
- first_name: Tatjana
full_name: Petrov, Tatjana
id: 3D5811FC-F248-11E8-B48F-1D18A9856A87
last_name: Petrov
orcid: 0000-0002-9041-0905
citation:
ama: Giacobbe M, Guet CC, Gupta A, Henzinger TA, Paixao T, Petrov T. Model checking
the evolution of gene regulatory networks. Acta Informatica. 2017;54(8):765-787.
doi:10.1007/s00236-016-0278-x
apa: Giacobbe, M., Guet, C. C., Gupta, A., Henzinger, T. A., Paixao, T., & Petrov,
T. (2017). Model checking the evolution of gene regulatory networks. Acta Informatica.
Springer. https://doi.org/10.1007/s00236-016-0278-x
chicago: Giacobbe, Mirco, Calin C Guet, Ashutosh Gupta, Thomas A Henzinger, Tiago
Paixao, and Tatjana Petrov. “Model Checking the Evolution of Gene Regulatory Networks.”
Acta Informatica. Springer, 2017. https://doi.org/10.1007/s00236-016-0278-x.
ieee: M. Giacobbe, C. C. Guet, A. Gupta, T. A. Henzinger, T. Paixao, and T. Petrov,
“Model checking the evolution of gene regulatory networks,” Acta Informatica,
vol. 54, no. 8. Springer, pp. 765–787, 2017.
ista: Giacobbe M, Guet CC, Gupta A, Henzinger TA, Paixao T, Petrov T. 2017. Model
checking the evolution of gene regulatory networks. Acta Informatica. 54(8), 765–787.
mla: Giacobbe, Mirco, et al. “Model Checking the Evolution of Gene Regulatory Networks.”
Acta Informatica, vol. 54, no. 8, Springer, 2017, pp. 765–87, doi:10.1007/s00236-016-0278-x.
short: M. Giacobbe, C.C. Guet, A. Gupta, T.A. Henzinger, T. Paixao, T. Petrov, Acta
Informatica 54 (2017) 765–787.
date_created: 2018-12-11T11:51:32Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2025-05-28T11:57:04Z
day: '01'
ddc:
- '006'
- '576'
department:
- _id: ToHe
- _id: CaGu
- _id: NiBa
doi: 10.1007/s00236-016-0278-x
ec_funded: 1
external_id:
isi:
- '000414343200003'
file:
- access_level: open_access
checksum: 4e661d9135d7f8c342e8e258dee76f3e
content_type: application/pdf
creator: dernst
date_created: 2019-01-17T15:57:29Z
date_updated: 2020-07-14T12:44:46Z
file_id: '5841'
file_name: 2017_ActaInformatica_Giacobbe.pdf
file_size: 755241
relation: main_file
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intvolume: ' 54'
isi: 1
issue: '8'
language:
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month: '12'
oa: 1
oa_version: Published Version
page: 765 - 787
project:
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call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
- _id: 25B1EC9E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '618091'
name: Speed of Adaptation in Population Genetics and Evolutionary Computation
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 25B07788-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '250152'
name: Limits to selection in biology and in evolutionary computation
publication: Acta Informatica
publication_identifier:
issn:
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publication_status: published
publisher: Springer
publist_id: '5898'
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quality_controlled: '1'
related_material:
record:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Model checking the evolution of gene regulatory networks
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: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 54
year: '2017'
...
---
_id: '1835'
abstract:
- lang: eng
text: The behaviour of gene regulatory networks (GRNs) is typically analysed using
simulation-based statistical testing-like methods. In this paper, we demonstrate
that we can replace this approach by a formal verification-like method that gives
higher assurance and scalability. We focus on Wagner’s weighted GRN model with
varying weights, which is used in evolutionary biology. In the model, weight parameters
represent the gene interaction strength that may change due to genetic mutations.
For a property of interest, we synthesise the constraints over the parameter space
that represent the set of GRNs satisfying the property. We experimentally show
that our parameter synthesis procedure computes the mutational robustness of GRNs
–an important problem of interest in evolutionary biology– more efficiently than
the classical simulation method. We specify the property in linear temporal logics.
We employ symbolic bounded model checking and SMT solving to compute the space
of GRNs that satisfy the property, which amounts to synthesizing a set of linear
constraints on the weights.
acknowledgement: "SNSF Early Postdoc.Mobility Fellowship, the grant number P2EZP2
148797.\r\n"
alternative_title:
- LNCS
author:
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Calin C
full_name: Guet, Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
- first_name: Ashutosh
full_name: Gupta, Ashutosh
id: 335E5684-F248-11E8-B48F-1D18A9856A87
last_name: Gupta
- 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: Tiago
full_name: Paixao, Tiago
id: 2C5658E6-F248-11E8-B48F-1D18A9856A87
last_name: Paixao
orcid: 0000-0003-2361-3953
- first_name: Tatjana
full_name: Petrov, Tatjana
id: 3D5811FC-F248-11E8-B48F-1D18A9856A87
last_name: Petrov
orcid: 0000-0002-9041-0905
citation:
ama: Giacobbe M, Guet CC, Gupta A, Henzinger TA, Paixao T, Petrov T. Model checking
gene regulatory networks. 2015;9035:469-483. doi:10.1007/978-3-662-46681-0_47
apa: 'Giacobbe, M., Guet, C. C., Gupta, A., Henzinger, T. A., Paixao, T., &
Petrov, T. (2015). Model checking gene regulatory networks. Presented at the TACAS:
Tools and Algorithms for the Construction and Analysis of Systems, London, United
Kingdom: Springer. https://doi.org/10.1007/978-3-662-46681-0_47'
chicago: Giacobbe, Mirco, Calin C Guet, Ashutosh Gupta, Thomas A Henzinger, Tiago
Paixao, and Tatjana Petrov. “Model Checking Gene Regulatory Networks.” Lecture
Notes in Computer Science. Springer, 2015. https://doi.org/10.1007/978-3-662-46681-0_47.
ieee: M. Giacobbe, C. C. Guet, A. Gupta, T. A. Henzinger, T. Paixao, and T. Petrov,
“Model checking gene regulatory networks,” vol. 9035. Springer, pp. 469–483, 2015.
ista: Giacobbe M, Guet CC, Gupta A, Henzinger TA, Paixao T, Petrov T. 2015. Model
checking gene regulatory networks. 9035, 469–483.
mla: Giacobbe, Mirco, et al. Model Checking Gene Regulatory Networks. Vol.
9035, Springer, 2015, pp. 469–83, doi:10.1007/978-3-662-46681-0_47.
short: M. Giacobbe, C.C. Guet, A. Gupta, T.A. Henzinger, T. Paixao, T. Petrov, 9035
(2015) 469–483.
conference:
end_date: 2015-04-18
location: London, United Kingdom
name: 'TACAS: Tools and Algorithms for the Construction and Analysis of Systems'
start_date: 2015-04-11
date_created: 2018-12-11T11:54:16Z
date_published: 2015-04-01T00:00:00Z
date_updated: 2025-05-28T11:57:04Z
day: '01'
department:
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doi: 10.1007/978-3-662-46681-0_47
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series_title: Lecture Notes in Computer Science
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title: Model checking gene regulatory networks
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volume: 9035
year: '2015'
...