---
_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: 2025-07-10T12:02:00Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3453483.3454076
ec_funded: 1
external_id:
isi:
- '000723661700050'
fulldoi: https://doi.org/10.1145/3453483.3454076
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 Probabilistic 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...