---
_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
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: 2024-03-28T23:30:34Z
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'
...