---
_id: '9645'
abstract:
- lang: eng
text: "We consider the fundamental problem of reachability analysis over imperative
programs with real variables. Previous works that tackle reachability are either
unable to handle programs consisting of general loops (e.g. symbolic execution),
or lack completeness guarantees (e.g. abstract interpretation), or are not automated
(e.g. incorrectness logic). In contrast, we propose a novel approach for reachability
analysis that can handle general and complex loops, is complete, and can be entirely
automated for a wide family of programs. Through the notion of Inductive Reachability
Witnesses (IRWs), our approach extends ideas from both invariant generation and
termination to reachability analysis.\r\n\r\nWe first show that our IRW-based
approach is sound and complete for reachability analysis of imperative programs.
Then, we focus on linear and polynomial programs and develop automated methods
for synthesizing linear and polynomial IRWs. In the linear case, we follow the
well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial
case, where we present a push-button semi-complete algorithm. We achieve this
using a novel combination of classical theorems in real algebraic geometry, such
as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally,
our experimental results show we can prove complex reachability objectives over
various benchmarks that were beyond the reach of previous methods."
acknowledgement: This research was partially supported by the ERC CoG 863818 (ForM-SMArt),
the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the
Huawei Innovation Research Program, the Facebook PhD Fellowship Program, and DOC
Fellowship No. 24956 of the Austrian Academy of Sciences (ÖAW).
article_processing_charge: No
author:
- first_name: Ali
full_name: Asadi, Ali
last_name: Asadi
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Mohammad
full_name: Mahdavi, Mohammad
last_name: Mahdavi
citation:
ama: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. Polynomial reachability
witnesses via Stellensätze. In: Proceedings of the 42nd ACM SIGPLAN International
Conference on Programming Language Design and Implementation. Association
for Computing Machinery; 2021:772-787. doi:10.1145/3453483.3454076'
apa: 'Asadi, A., Chatterjee, K., Fu, H., Goharshady, A. K., & Mahdavi, M. (2021).
Polynomial reachability witnesses via Stellensätze. In Proceedings of the 42nd
ACM SIGPLAN International Conference on Programming Language Design and Implementation
(pp. 772–787). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454076'
chicago: Asadi, Ali, Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady,
and Mohammad Mahdavi. “Polynomial Reachability Witnesses via Stellensätze.” In
Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation, 772–87. Association for Computing Machinery,
2021. https://doi.org/10.1145/3453483.3454076.
ieee: A. Asadi, K. Chatterjee, H. Fu, A. K. Goharshady, and M. Mahdavi, “Polynomial
reachability witnesses via Stellensätze,” in Proceedings of the 42nd ACM SIGPLAN
International Conference on Programming Language Design and Implementation,
Online, 2021, pp. 772–787.
ista: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. 2021. Polynomial reachability
witnesses via Stellensätze. Proceedings of the 42nd ACM SIGPLAN International
Conference on Programming Language Design and Implementation. PLDI: Programming
Language Design and Implementation, 772–787.'
mla: Asadi, Ali, et al. “Polynomial Reachability Witnesses via Stellensätze.” Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 772–87,
doi:10.1145/3453483.3454076.
short: A. Asadi, K. Chatterjee, H. Fu, A.K. Goharshady, M. Mahdavi, in:, Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 772–787.
conference:
end_date: 2021-06-26
location: Online
name: ' PLDI: Programming Language Design and Implementation'
start_date: 2021-06-20
date_created: 2021-07-11T22:01:17Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2025-07-14T09:10:06Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3453483.3454076
ec_funded: 1
external_id:
isi:
- '000723661700050'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.archives-ouvertes.fr/hal-03183862/
month: '06'
oa: 1
oa_version: Submitted Version
page: 772-787
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 267066CE-B435-11E9-9278-68D0E5697425
name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies
publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation
publication_identifier:
isbn:
- '9781450383912'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Polynomial reachability witnesses via Stellensätze
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '9646'
abstract:
- lang: eng
text: We consider the fundamental problem of deriving quantitative bounds on the
probability that a given assertion is violated in a probabilistic program. We
provide automated algorithms that obtain both lower and upper bounds on the assertion
violation probability. The main novelty of our approach is that we prove new and
dedicated fixed-point theorems which serve as the theoretical basis of our algorithms
and enable us to reason about assertion violation bounds in terms of pre and post
fixed-point functions. To synthesize such fixed-points, we devise algorithms that
utilize a wide range of mathematical tools, including repulsing ranking supermartingales,
Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization.
On the theoretical side, we provide (i) the first automated algorithm for lower-bounds
on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds
of exponential form in affine programs, and (iii) provably and significantly tighter
upper-bounds than the previous approaches. On the practical side, we show our
algorithms can handle a wide variety of programs from the literature and synthesize
bounds that are remarkably tighter than previous results, in some cases by thousands
of orders of magnitude.
acknowledgement: 'We are very thankful to the anonymous reviewers for the helpful
and valuable comments. The work was partially supported by the National Natural
Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research
Program, the ERC CoG 863818 (ForM-SMArt), the Facebook PhD Fellowship Program and
DOC Fellowship #24956 of the Austrian Academy of Sciences (ÖAW).'
article_processing_charge: No
arxiv: 1
author:
- first_name: Jinyi
full_name: Wang, Jinyi
last_name: Wang
- first_name: Yican
full_name: Sun, Yican
last_name: Sun
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
citation:
ama: 'Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. Quantitative analysis of
assertion violations in probabilistic programs. In: Proceedings of the 42nd
ACM SIGPLAN International Conference on Programming Language Design and Implementation.
Association for Computing Machinery; 2021:1171-1186. doi:10.1145/3453483.3454102'
apa: 'Wang, J., Sun, Y., Fu, H., Chatterjee, K., & Goharshady, A. K. (2021).
Quantitative analysis of assertion violations in probabilistic programs. In Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation (pp. 1171–1186). Online: Association for Computing Machinery.
https://doi.org/10.1145/3453483.3454102'
chicago: Wang, Jinyi, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar
Goharshady. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.”
In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation, 1171–86. Association for Computing Machinery,
2021. https://doi.org/10.1145/3453483.3454102.
ieee: J. Wang, Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Quantitative
analysis of assertion violations in probabilistic programs,” in Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Online, 2021, pp. 1171–1186.
ista: 'Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. 2021. Quantitative analysis
of assertion violations in probabilistic programs. Proceedings of the 42nd ACM
SIGPLAN International Conference on Programming Language Design and Implementation.
PLDI: Programming Language Design and Implementation, 1171–1186.'
mla: Wang, Jinyi, et al. “Quantitative Analysis of Assertion Violations in Probabilistic
Programs.” Proceedings of the 42nd ACM SIGPLAN International Conference on
Programming Language Design and Implementation, Association for Computing
Machinery, 2021, pp. 1171–86, doi:10.1145/3453483.3454102.
short: J. Wang, Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 1171–1186.
conference:
end_date: 2021-06-26
location: Online
name: 'PLDI: Programming Language Design and Implementation'
start_date: 2021-06-20
date_created: 2021-07-11T22:01:18Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2025-07-14T09:10:06Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3453483.3454102
ec_funded: 1
external_id:
arxiv:
- '2011.14617'
isi:
- '000723661700076'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2011.14617
month: '06'
oa: 1
oa_version: Preprint
page: 1171-1186
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 267066CE-B435-11E9-9278-68D0E5697425
name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies
publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation
publication_identifier:
isbn:
- '9781450383912'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative analysis of assertion violations in probabilistic programs
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '8089'
abstract:
- lang: eng
text: "We consider the classical problem of invariant generation for programs with
polynomial assignments and focus on synthesizing invariants that are a conjunction
of strict polynomial inequalities. We present a sound and semi-complete method
based on positivstellensaetze, i.e. theorems in semi-algebraic geometry that characterize
positive polynomials over a semi-algebraic set.\r\n\r\nOn the theoretical side,
the worst-case complexity of our approach is subexponential, whereas the worst-case
complexity of the previous complete method (Kapur, ACA 2004) is doubly-exponential.
Even when restricted to linear invariants, the best previous complexity for complete
invariant generation is exponential (Colon et al, CAV 2003). On the practical
side, we reduce the invariant generation problem to quadratic programming (QCLP),
which is a classical optimization problem with many industrial solvers. We demonstrate
the applicability of our approach by providing experimental results on several
academic benchmarks. To the best of our knowledge, the only previous invariant
generation method that provides completeness guarantees for invariants consisting
of polynomial inequalities is (Kapur, ACA 2004), which relies on quantifier elimination
and cannot even handle toy programs such as our running example."
article_processing_charge: No
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Ehsan Kafshdar
full_name: Goharshady, Ehsan Kafshdar
last_name: Goharshady
citation:
ama: 'Chatterjee K, Fu H, Goharshady AK, Goharshady EK. Polynomial invariant generation
for non-deterministic recursive programs. In: Proceedings of the 41st ACM SIGPLAN
Conference on Programming Language Design and Implementation. Association
for Computing Machinery; 2020:672-687. doi:10.1145/3385412.3385969'
apa: 'Chatterjee, K., Fu, H., Goharshady, A. K., & Goharshady, E. K. (2020).
Polynomial invariant generation for non-deterministic recursive programs. In Proceedings
of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation
(pp. 672–687). London, United Kingdom: Association for Computing Machinery. https://doi.org/10.1145/3385412.3385969'
chicago: Chatterjee, Krishnendu, Hongfei Fu, Amir Kafshdar Goharshady, and Ehsan
Kafshdar Goharshady. “Polynomial Invariant Generation for Non-Deterministic Recursive
Programs.” In Proceedings of the 41st ACM SIGPLAN Conference on Programming
Language Design and Implementation, 672–87. Association for Computing Machinery,
2020. https://doi.org/10.1145/3385412.3385969.
ieee: K. Chatterjee, H. Fu, A. K. Goharshady, and E. K. Goharshady, “Polynomial
invariant generation for non-deterministic recursive programs,” in Proceedings
of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation,
London, United Kingdom, 2020, pp. 672–687.
ista: 'Chatterjee K, Fu H, Goharshady AK, Goharshady EK. 2020. Polynomial invariant
generation for non-deterministic recursive programs. Proceedings of the 41st ACM
SIGPLAN Conference on Programming Language Design and Implementation. PLDI: Programming
Language Design and Implementation, 672–687.'
mla: Chatterjee, Krishnendu, et al. “Polynomial Invariant Generation for Non-Deterministic
Recursive Programs.” Proceedings of the 41st ACM SIGPLAN Conference on Programming
Language Design and Implementation, Association for Computing Machinery, 2020,
pp. 672–87, doi:10.1145/3385412.3385969.
short: K. Chatterjee, H. Fu, A.K. Goharshady, E.K. Goharshady, in:, Proceedings
of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation,
Association for Computing Machinery, 2020, pp. 672–687.
conference:
end_date: 2020-06-20
location: London, United Kingdom
name: 'PLDI: Programming Language Design and Implementation'
start_date: 2020-06-15
date_created: 2020-07-05T22:00:45Z
date_published: 2020-06-11T00:00:00Z
date_updated: 2025-06-02T08:53:42Z
day: '11'
department:
- _id: KrCh
doi: 10.1145/3385412.3385969
external_id:
arxiv:
- '1902.04373'
isi:
- '000614622300045'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.04373
month: '06'
oa: 1
oa_version: Preprint
page: 672-687
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
publication: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language
Design and Implementation
publication_identifier:
isbn:
- '9781450376136'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
record:
- id: '8934'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Polynomial invariant generation for non-deterministic recursive programs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2020'
...
---
_id: '6175'
abstract:
- lang: eng
text: "We consider the problem of expected cost analysis over nondeterministic probabilistic
programs,\r\nwhich aims at automated methods for analyzing the resource-usage
of such programs.\r\nPrevious approaches for this problem could only handle nonnegative
bounded costs.\r\nHowever, in many scenarios, such as queuing networks or analysis
of cryptocurrency protocols,\r\nboth positive and negative costs are necessary
and the costs are unbounded as well.\r\n\r\nIn this work, we present a sound and
efficient approach to obtain polynomial bounds on the\r\nexpected accumulated
cost of nondeterministic probabilistic programs.\r\nOur approach can handle (a)
general positive and negative costs with bounded updates in\r\nvariables; and
(b) nonnegative costs with general updates to variables.\r\nWe show that several
natural examples which could not be\r\nhandled by previous approaches are captured
in our framework.\r\n\r\nMoreover, our approach leads to an efficient polynomial-time
algorithm, while no\r\nprevious approach for cost analysis of probabilistic programs
could guarantee polynomial runtime.\r\nFinally, we show the effectiveness of our
approach using experimental results on a variety of programs for which we efficiently
synthesize tight resource-usage bounds."
article_processing_charge: No
arxiv: 1
author:
- first_name: Peixin
full_name: Wang, Peixin
last_name: Wang
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Xudong
full_name: Qin, Xudong
last_name: Qin
- first_name: Wenjun
full_name: Shi, Wenjun
last_name: Shi
citation:
ama: 'Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. Cost analysis of
nondeterministic probabilistic programs. In: PLDI 2019: Proceedings of the
40th ACM SIGPLAN Conference on Programming Language Design and Implementation.
Association for Computing Machinery; 2019:204-220. doi:10.1145/3314221.3314581'
apa: 'Wang, P., Fu, H., Goharshady, A. K., Chatterjee, K., Qin, X., & Shi, W.
(2019). Cost analysis of nondeterministic probabilistic programs. In PLDI 2019:
Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design
and Implementation (pp. 204–220). Phoenix, AZ, United States: Association
for Computing Machinery. https://doi.org/10.1145/3314221.3314581'
chicago: 'Wang, Peixin, Hongfei Fu, Amir Kafshdar Goharshady, Krishnendu Chatterjee,
Xudong Qin, and Wenjun Shi. “Cost Analysis of Nondeterministic Probabilistic Programs.”
In PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming
Language Design and Implementation, 204–20. Association for Computing Machinery,
2019. https://doi.org/10.1145/3314221.3314581.'
ieee: 'P. Wang, H. Fu, A. K. Goharshady, K. Chatterjee, X. Qin, and W. Shi, “Cost
analysis of nondeterministic probabilistic programs,” in PLDI 2019: Proceedings
of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation,
Phoenix, AZ, United States, 2019, pp. 204–220.'
ista: 'Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. 2019. Cost analysis
of nondeterministic probabilistic programs. PLDI 2019: Proceedings of the 40th
ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI:
Conference on Programming Language Design and Implementation, 204–220.'
mla: 'Wang, Peixin, et al. “Cost Analysis of Nondeterministic Probabilistic Programs.”
PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language
Design and Implementation, Association for Computing Machinery, 2019, pp.
204–20, doi:10.1145/3314221.3314581.'
short: 'P. Wang, H. Fu, A.K. Goharshady, K. Chatterjee, X. Qin, W. Shi, in:, PLDI
2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2019, pp. 204–220.'
conference:
end_date: 2019-06-26
location: Phoenix, AZ, United States
name: 'PLDI: Conference on Programming Language Design and Implementation'
start_date: 2019-06-22
date_created: 2019-03-25T10:13:25Z
date_published: 2019-06-08T00:00:00Z
date_updated: 2025-06-02T08:53:45Z
day: '08'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.1145/3314221.3314581
ec_funded: 1
external_id:
arxiv:
- '1902.04659'
isi:
- '000523190300014'
file:
- access_level: open_access
checksum: 703a5e9b8c8587f2a44085ffd9a4db64
content_type: application/pdf
creator: akafshda
date_created: 2019-03-25T10:11:22Z
date_updated: 2020-07-14T12:47:20Z
file_id: '6176'
file_name: paper.pdf
file_size: 4051066
relation: main_file
file_date_updated: 2020-07-14T12:47:20Z
has_accepted_license: '1'
isi: 1
keyword:
- Program Cost Analysis
- Program Termination
- Probabilistic Programs
- Martingales
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 204-220
project:
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 266EEEC0-B435-11E9-9278-68D0E5697425
name: Quantitative Game-theoretic Analysis of Blockchain Applications and Smart
Contracts
publication: 'PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming
Language Design and Implementation'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
record:
- id: '5457'
relation: earlier_version
status: public
- id: '8934'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Cost analysis of nondeterministic probabilistic programs
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2019'
...
---
_id: '5977'
abstract:
- lang: eng
text: 'We consider the stochastic shortest path (SSP)problem for succinct Markov
decision processes(MDPs), where the MDP consists of a set of vari-ables, and a
set of nondeterministic rules that up-date the variables. First, we show that
several ex-amples from the AI literature can be modeled assuccinct MDPs. Then
we present computationalapproaches for upper and lower bounds for theSSP problem:
(a) for computing upper bounds, ourmethod is polynomial-time in the implicit descrip-tion
of the MDP; (b) for lower bounds, we present apolynomial-time (in the size of
the implicit descrip-tion) reduction to quadratic programming. Our ap-proach is
applicable even to infinite-state MDPs.Finally, we present experimental results
to demon-strate the effectiveness of our approach on severalclassical examples
from the AI literature.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir
full_name: Goharshady, Amir
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Nastaran
full_name: Okati, Nastaran
last_name: Okati
citation:
ama: 'Chatterjee K, Fu H, Goharshady AK, Okati N. Computational approaches for stochastic
shortest path on succinct MDPs. In: Proceedings of the Twenty-Seventh International
Joint Conference on Artificial Intelligence. Vol 2018. IJCAI; 2018:4700-4707.
doi:10.24963/ijcai.2018/653'
apa: 'Chatterjee, K., Fu, H., Goharshady, A. K., & Okati, N. (2018). Computational
approaches for stochastic shortest path on succinct MDPs. In Proceedings of
the Twenty-Seventh International Joint Conference on Artificial Intelligence
(Vol. 2018, pp. 4700–4707). Stockholm, Sweden: IJCAI. https://doi.org/10.24963/ijcai.2018/653'
chicago: Chatterjee, Krishnendu, Hongfei Fu, Amir Kafshdar Goharshady, and Nastaran
Okati. “Computational Approaches for Stochastic Shortest Path on Succinct MDPs.”
In Proceedings of the Twenty-Seventh International Joint Conference on Artificial
Intelligence, 2018:4700–4707. IJCAI, 2018. https://doi.org/10.24963/ijcai.2018/653.
ieee: K. Chatterjee, H. Fu, A. K. Goharshady, and N. Okati, “Computational approaches
for stochastic shortest path on succinct MDPs,” in Proceedings of the Twenty-Seventh
International Joint Conference on Artificial Intelligence, Stockholm, Sweden,
2018, vol. 2018, pp. 4700–4707.
ista: 'Chatterjee K, Fu H, Goharshady AK, Okati N. 2018. Computational approaches
for stochastic shortest path on succinct MDPs. Proceedings of the Twenty-Seventh
International Joint Conference on Artificial Intelligence. IJCAI: International
Joint Conference on Artificial Intelligence vol. 2018, 4700–4707.'
mla: Chatterjee, Krishnendu, et al. “Computational Approaches for Stochastic Shortest
Path on Succinct MDPs.” Proceedings of the Twenty-Seventh International Joint
Conference on Artificial Intelligence, vol. 2018, IJCAI, 2018, pp. 4700–07,
doi:10.24963/ijcai.2018/653.
short: K. Chatterjee, H. Fu, A.K. Goharshady, N. Okati, in:, Proceedings of the
Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI,
2018, pp. 4700–4707.
conference:
end_date: 2018-07-19
location: Stockholm, Sweden
name: 'IJCAI: International Joint Conference on Artificial Intelligence'
start_date: 2018-07-13
date_created: 2019-02-13T13:26:27Z
date_published: 2018-07-17T00:00:00Z
date_updated: 2025-06-02T08:53:44Z
day: '17'
department:
- _id: KrCh
doi: 10.24963/ijcai.2018/653
ec_funded: 1
external_id:
arxiv:
- '1804.08984'
isi:
- '000764175404118'
intvolume: ' 2018'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.08984
month: '07'
oa: 1
oa_version: Preprint
page: 4700-4707
project:
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Proceedings of the Twenty-Seventh International Joint Conference on Artificial
Intelligence
publication_identifier:
isbn:
- 978-099924112-7
issn:
- '10450823'
publication_status: published
publisher: IJCAI
quality_controlled: '1'
related_material:
record:
- id: '8934'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Computational approaches for stochastic shortest path on succinct MDPs
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 2018
year: '2018'
...
---
_id: '5993'
abstract:
- lang: eng
text: 'In this article, we consider the termination problem of probabilistic programs
with real-valued variables. Thequestions concerned are: qualitative ones that
ask (i) whether the program terminates with probability 1(almost-sure termination)
and (ii) whether the expected termination time is finite (finite termination);
andquantitative ones that ask (i) to approximate the expected termination time
(expectation problem) and (ii) tocompute a boundBsuch that the probability not
to terminate afterBsteps decreases exponentially (con-centration problem). To
solve these questions, we utilize the notion of ranking supermartingales, which
isa powerful approach for proving termination of probabilistic programs. In detail,
we focus on algorithmicsynthesis of linear ranking-supermartingales over affine
probabilistic programs (Apps) with both angelic anddemonic non-determinism. An
important subclass of Apps is LRApp which is defined as the class of all Appsover
which a linear ranking-supermartingale exists.Our main contributions are as follows.
Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial
time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor
Apps with angelic non-determinism. Moreover, theNP-hardness result holds already
for Appswithout probability and demonic non-determinism. Secondly, we show that
the concentration problem overLRApp can be solved in the same complexity as for
the membership problem of LRApp. Finally, we show thatthe expectation problem
over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability
and non-determinism (i.e., deterministic programs). Our experimental results demonstrate
theeffectiveness of our approach to answer the qualitative and quantitative questions
over Apps with at mostdemonic non-determinism.'
article_number: '7'
article_processing_charge: No
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Petr
full_name: Novotný, Petr
id: 3CC3B868-F248-11E8-B48F-1D18A9856A87
last_name: Novotný
- first_name: Rouzbeh
full_name: Hasheminezhad, Rouzbeh
last_name: Hasheminezhad
citation:
ama: Chatterjee K, Fu H, Novotný P, Hasheminezhad R. Algorithmic analysis of qualitative
and quantitative termination problems for affine probabilistic programs. ACM
Transactions on Programming Languages and Systems. 2018;40(2). doi:10.1145/3174800
apa: Chatterjee, K., Fu, H., Novotný, P., & Hasheminezhad, R. (2018). Algorithmic
analysis of qualitative and quantitative termination problems for affine probabilistic
programs. ACM Transactions on Programming Languages and Systems. Association
for Computing Machinery (ACM). https://doi.org/10.1145/3174800
chicago: Chatterjee, Krishnendu, Hongfei Fu, Petr Novotný, and Rouzbeh Hasheminezhad.
“Algorithmic Analysis of Qualitative and Quantitative Termination Problems for
Affine Probabilistic Programs.” ACM Transactions on Programming Languages and
Systems. Association for Computing Machinery (ACM), 2018. https://doi.org/10.1145/3174800.
ieee: K. Chatterjee, H. Fu, P. Novotný, and R. Hasheminezhad, “Algorithmic analysis
of qualitative and quantitative termination problems for affine probabilistic
programs,” ACM Transactions on Programming Languages and Systems, vol.
40, no. 2. Association for Computing Machinery (ACM), 2018.
ista: Chatterjee K, Fu H, Novotný P, Hasheminezhad R. 2018. Algorithmic analysis
of qualitative and quantitative termination problems for affine probabilistic
programs. ACM Transactions on Programming Languages and Systems. 40(2), 7.
mla: Chatterjee, Krishnendu, et al. “Algorithmic Analysis of Qualitative and Quantitative
Termination Problems for Affine Probabilistic Programs.” ACM Transactions on
Programming Languages and Systems, vol. 40, no. 2, 7, Association for Computing
Machinery (ACM), 2018, doi:10.1145/3174800.
short: K. Chatterjee, H. Fu, P. Novotný, R. Hasheminezhad, ACM Transactions on Programming
Languages and Systems 40 (2018).
date_created: 2019-02-14T12:29:10Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-19T14:38:42Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3174800
ec_funded: 1
external_id:
arxiv:
- '1510.08517'
isi:
- '000434634500003'
intvolume: ' 40'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1510.08517
month: '06'
oa: 1
oa_version: Submitted Version
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: ACM Transactions on Programming Languages and Systems
publication_identifier:
issn:
- 0164-0925
publication_status: published
publisher: Association for Computing Machinery (ACM)
quality_controlled: '1'
related_material:
record:
- id: '1438'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Algorithmic analysis of qualitative and quantitative termination problems for
affine probabilistic programs
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 40
year: '2018'
...
---
_id: '1438'
abstract:
- lang: eng
text: 'In this paper, we consider termination of probabilistic programs with real-valued
variables. The questions concerned are: (a) qualitative ones that ask (i) whether
the program terminates with probability 1 (almost-sure termination) and (ii) whether
the expected termination time is finite (finite termination); (b) quantitative
ones that ask (i) to approximate the expected termination time (expectation problem)
and (ii) to compute a bound B such that the probability to terminate after B steps
decreases exponentially (concentration problem). To solve these questions, we
utilize the notion of ranking supermartingales which is a powerful approach for
proving termination of probabilistic programs. In detail, we focus on algorithmic
synthesis of linear ranking-supermartingales over affine probabilistic programs
(APP''s) with both angelic and demonic non-determinism. An important subclass
of APP''s is LRAPP which is defined as the class of all APP''s over which a linear
ranking-supermartingale exists. Our main contributions are as follows. Firstly,
we show that the membership problem of LRAPP (i) can be decided in polynomial
time for APP''s with at most demonic non-determinism, and (ii) is NP-hard and
in PSPACE for APP''s with angelic non-determinism; moreover, the NP-hardness result
holds already for APP''s without probability and demonic non-determinism. Secondly,
we show that the concentration problem over LRAPP can be solved in the same complexity
as for the membership problem of LRAPP. Finally, we show that the expectation
problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP''s
without probability and non-determinism (i.e., deterministic programs). Our experimental
results demonstrate the effectiveness of our approach to answer the qualitative
and quantitative questions over APP''s with at most demonic non-determinism.'
acknowledgement: 'Supported by the Natural Science Foundation of China (NSFC) under
Grant No. 61532019 '
alternative_title:
- POPL
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Petr
full_name: Novotny, Petr
id: 3CC3B868-F248-11E8-B48F-1D18A9856A87
last_name: Novotny
- first_name: Rouzbeh
full_name: Hasheminezhad, Rouzbeh
last_name: Hasheminezhad
citation:
ama: 'Chatterjee K, Fu H, Novotný P, Hasheminezhad R. Algorithmic analysis of qualitative
and quantitative termination problems for affine probabilistic programs. In: Vol
20-22. ACM; 2016:327-342. doi:10.1145/2837614.2837639'
apa: 'Chatterjee, K., Fu, H., Novotný, P., & Hasheminezhad, R. (2016). Algorithmic
analysis of qualitative and quantitative termination problems for affine probabilistic
programs (Vol. 20–22, pp. 327–342). Presented at the POPL: Principles of Programming
Languages, St. Petersburg, FL, USA: ACM. https://doi.org/10.1145/2837614.2837639'
chicago: Chatterjee, Krishnendu, Hongfei Fu, Petr Novotný, and Rouzbeh Hasheminezhad.
“Algorithmic Analysis of Qualitative and Quantitative Termination Problems for
Affine Probabilistic Programs,” 20–22:327–42. ACM, 2016. https://doi.org/10.1145/2837614.2837639.
ieee: 'K. Chatterjee, H. Fu, P. Novotný, and R. Hasheminezhad, “Algorithmic analysis
of qualitative and quantitative termination problems for affine probabilistic
programs,” presented at the POPL: Principles of Programming Languages, St. Petersburg,
FL, USA, 2016, vol. 20–22, pp. 327–342.'
ista: 'Chatterjee K, Fu H, Novotný P, Hasheminezhad R. 2016. Algorithmic analysis
of qualitative and quantitative termination problems for affine probabilistic
programs. POPL: Principles of Programming Languages, POPL, vol. 20–22, 327–342.'
mla: Chatterjee, Krishnendu, et al. Algorithmic Analysis of Qualitative and Quantitative
Termination Problems for Affine Probabilistic Programs. Vol. 20–22, ACM, 2016,
pp. 327–42, doi:10.1145/2837614.2837639.
short: K. Chatterjee, H. Fu, P. Novotný, R. Hasheminezhad, in:, ACM, 2016, pp. 327–342.
conference:
end_date: 2016-01-22
location: St. Petersburg, FL, USA
name: 'POPL: Principles of Programming Languages'
start_date: 2016-01-20
date_created: 2018-12-11T11:52:01Z
date_published: 2016-01-11T00:00:00Z
date_updated: 2023-09-19T14:38:41Z
day: '11'
department:
- _id: KrCh
doi: 10.1145/2837614.2837639
ec_funded: 1
external_id:
arxiv:
- '1510.08517'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.08517
month: '01'
oa: 1
oa_version: Preprint
page: 327 - 342
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication_status: published
publisher: ACM
publist_id: '5760'
quality_controlled: '1'
related_material:
record:
- id: '5993'
relation: later_version
status: public
scopus_import: 1
status: public
title: Algorithmic analysis of qualitative and quantitative termination problems for
affine probabilistic programs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20-22
year: '2016'
...
---
_id: '1386'
abstract:
- lang: eng
text: We consider nondeterministic probabilistic programs with the most basic liveness
property of termination. We present efficient methods for termination analysis
of nondeterministic probabilistic programs with polynomial guards and assignments.
Our approach is through synthesis of polynomial ranking supermartingales, that
on one hand significantly generalizes linear ranking supermartingales and on the
other hand is a counterpart of polynomial ranking-functions for proving termination
of nonprobabilistic programs. The approach synthesizes polynomial ranking-supermartingales
through Positivstellensatz's, yielding an efficient method which is not only sound,
but also semi-complete over a large subclass of programs. We show experimental
results to demonstrate that our approach can handle several classical programs
with complex polynomial guards and assignments, and can synthesize efficient quadratic
ranking-supermartingales when a linear one does not exist even for simple affine
programs.
alternative_title:
- LNCS
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir
full_name: Goharshady, Amir
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
citation:
ama: 'Chatterjee K, Fu H, Goharshady AK. Termination analysis of probabilistic programs
through Positivstellensatz’s. In: Vol 9779. Springer; 2016:3-22. doi:10.1007/978-3-319-41528-4_1'
apa: 'Chatterjee, K., Fu, H., & Goharshady, A. K. (2016). Termination analysis
of probabilistic programs through Positivstellensatz’s (Vol. 9779, pp. 3–22).
Presented at the CAV: Computer Aided Verification, Toronto, Canada: Springer.
https://doi.org/10.1007/978-3-319-41528-4_1'
chicago: Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Termination
Analysis of Probabilistic Programs through Positivstellensatz’s,” 9779:3–22. Springer,
2016. https://doi.org/10.1007/978-3-319-41528-4_1.
ieee: 'K. Chatterjee, H. Fu, and A. K. Goharshady, “Termination analysis of probabilistic
programs through Positivstellensatz’s,” presented at the CAV: Computer Aided Verification,
Toronto, Canada, 2016, vol. 9779, pp. 3–22.'
ista: 'Chatterjee K, Fu H, Goharshady AK. 2016. Termination analysis of probabilistic
programs through Positivstellensatz’s. CAV: Computer Aided Verification, LNCS,
vol. 9779, 3–22.'
mla: Chatterjee, Krishnendu, et al. Termination Analysis of Probabilistic Programs
through Positivstellensatz’s. Vol. 9779, Springer, 2016, pp. 3–22, doi:10.1007/978-3-319-41528-4_1.
short: K. Chatterjee, H. Fu, A.K. Goharshady, in:, Springer, 2016, pp. 3–22.
conference:
end_date: 2016-07-23
location: Toronto, Canada
name: 'CAV: Computer Aided Verification'
start_date: 2016-07-17
date_created: 2018-12-11T11:51:43Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2024-03-25T23:30:18Z
day: '01'
department:
- _id: KrCh
doi: 10.1007/978-3-319-41528-4_1
ec_funded: 1
intvolume: ' 9779'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1604.07169
month: '07'
oa: 1
oa_version: Preprint
page: 3 - 22
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
publication_status: published
publisher: Springer
publist_id: '5824'
quality_controlled: '1'
related_material:
record:
- id: '8934'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Termination analysis of probabilistic programs through Positivstellensatz's
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9779
year: '2016'
...