research-article

Proofs that count

Authors:

Zachary Kincaid,

Andreas PodelskiAuthors Info & Claims

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 151 - 164

https://doi.org/10.1145/2535838.2535885

Published: 08 January 2014 Publication History

Abstract

Counting arguments are among the most basic proof methods in mathematics. Within the field of formal verification, they are useful for reasoning about programs with infinite control, such as programs with an unbounded number of threads, or (concurrent) programs with recursive procedures. While counting arguments are common in informal, hand-written proofs of such programs, there are no fully automated techniques to construct counting arguments. The key questions involved in automating counting arguments are: how to decide what should be counted?, and how to decide when a counting argument is valid? In this paper, we present a technique for automatically constructing and checking counting arguments, which includes novel solutions to these questions.

Supplementary Material

MP4 File (d1_left_t9.mp4)

Download
198.38 MB

References

[1]

P. A. Abdulla, A. Bouajjani, B. Jonsson, and M. Nilsson. Handling global conditions in parameterized system verification. In CAV, pages 134--145, 1999.

Digital Library

[2]

P. A. Abdulla, Y.-F. Chen, G. Delzanno, F. Haziza, C.-D. Hong, and A. Rezine. Constrained monotonic abstraction: a cegar for parameterized verification. In CONCUR, pages 86--101, 2010.

Digital Library

[3]

P. A. Abdulla, F. Haziza, and L. Holík. All for the price of few. In VMCAI, pages 476--495, 2013.

Digital Library

[4]

K. R. Apt and D. Kozen. Limits for automatic verification of finitestate concurrent systems. Inf. Process. Lett., 22(6):307--309, 1986.

Digital Library

[5]

T. Arons, A. Pnueli, S. Ruah, J. Xu, and L. D. Zuck. Parameterized verification with automatically computed inductive assertions. In CAV, pages 221--234, 2001.

Digital Library

[6]

T. Ball, S. Chaki, and S. K. Rajamani. Parameterized verification of multithreaded software libraries. In TACAS, pages 158--173, 2001.

Digital Library

[7]

S. Bardin, A. Finkel, J. Leroux, and L. Petrucci. Fast: acceleration from theory to practice. Int. J. Softw. Tools Technol. Transf., 10(5): 401--424, Sept. 2008.

Digital Library

[8]

K. Baukus, S. Bensalem, Y. Lakhnech, and K. Stahl. Abstracting WS1S systems to verify parameterized networks. In TACAS, pages 188--203, 2000.

Digital Library

[9]

K. Baukus, K. Stahl, S. Bensalem, and Y. Lakhnech. Networks of processes with parameterized state space. Electr. Notes Theor. Comput. Sci., 50(4):386--400, 2001.

[10]

J. Berdine, T. Lev-Ami, R. Manevich, G. Ramalingam, and M. Sagiv. Thread quantification for concurrent shape analysis. In CAV, pages 399--413, 2008.

Digital Library

[11]

A. Bouajjani, B. Jonsson, M. Nilsson, and T. Touili. Regular model checking. In CAV, pages 403--418, 2000.

Digital Library

[12]

A. R. Bradley. Sat-based model checking without unrolling. In VMCAI, pages 70--87, 2011.

Digital Library

[13]

E. M. Clarke, O. Grumberg, and M. C. Browne. Reasoning about networks with many identical finite-state processes. In PODC, pages 240--248, 1986.

Digital Library

[14]

E. M. Clarke, O. Grumberg, and S. Jha. Veryfying parameterized networks using abstraction and regular languages. In CONCUR, pages 395--407, 1995.

Digital Library

[15]

M. A. Colón, S. Sankaranarayanan, and H. B. Sipma. Linear invariant generation using non-linear constraint solving. In Computer Aided Verification, pages 420--432, 2003.

[16]

G. Delzanno, J.-F. Raskin, and L. V. Begin. Towards the automated verification of multithreaded java programs. In TACAS, pages 173--187, 2002.

Digital Library

[17]

T. Elmas, S. Qadeer, and S. Tasiran. A calculus of atomic actions. In POPL, pages 2--15, 2009.

Digital Library

[18]

A. Farzan and Z. Kincaid. Verification of parameterized concurrent programs by modular reasoning about data and control. In POPL, pages 297--308, 2012.

Digital Library

[19]

A. Farzan, Z. Kincaid, and A. Podelski. Inductive data flow graphs. In POPL, pages 129--142, 2013.

Digital Library

[20]

D. Fisman and A. Pnueli. Beyond regular model checking. In FSTTCS, pages 156--170, 2001.

Digital Library

[21]

P. Ganty, R. Majumdar, and B. Monmege. Bounded underapproximations. Formal Methods in System Design, 40(2):206--231, 2012.

Digital Library

[22]

S. M. German and A. P. Sistla. Reasoning about systems with many processes. J. ACM, 39(3):675--735, 1992.

Digital Library

[23]

A. Gupta, C. Popeea, and A. Rybalchenko. Predicate abstraction and refinement for verifying multi-threaded programs. In POPL, pages 331--344, 2011.

Digital Library

[24]

M. Hack. Decidability questions for Petri nets. PhD thesis, MIT, June 1976.

[25]

M. Heizmann, J. Hoenicke, and A. Podelski. Refinement of trace abstraction. In SAS, pages 69--85, 2009.

Digital Library

[26]

L. E. Holloway, B. H. Krogh, and A. Giua. A survey of petri net methods for controlled discrete eventsystems. Discrete Event Dynamic Systems, 7(2):151--190, Apr. 1997.

Digital Library

[27]

C. N. Ip and D. L. Dill. Verifying systems with replicated components in mur'. Formal Methods in System Design, 14(3):273--310, 1999.

Digital Library

[28]

A. John, I. Konnov, U. Schmid, H. Veith, and J.Widder. Parameterized model checking of fault-tolerant distributed algorithms by abstraction. In FMCAD, pages 201--209, 2013.

[29]

A. Kaiser, D. Kroening, and T. Wahl. Dynamic cutoff detection in parameterized concurrent programs. In CAV, pages 645--659, 2010.

Digital Library

[30]

R. M. Karp and R. E. Miller. Parallel program schemata. J. Comput. Syst. Sci., 3(2):147--195, 1969.

Digital Library

[31]

Y. Kesten, A. Pnueli, E. Shahar, and L. D. Zuck. Network invariants in action. In CONCUR, pages 101--115, 2002.

Digital Library

[32]

S. R. Kosaraju. Decidability of reachability in vector addition systems (preliminary version). In STOC, pages 267--281, 1982.

Digital Library

[33]

R. P. Kurshan and K. L. McMillan. A structural induction theorem for processes. Inf. Comput., 117(1):1--11, 1995.

Digital Library

[34]

S. La Torre, P. Madhusudan, and G. Parlato. Model-checking parameterized concurrent programs using linear interfaces. In CAV, pages 629--644, 2010.

Digital Library

[35]

J. Leroux. Vector addition system reachability problem: a short selfcontained proof. In POPL, pages 307--316, 2011.

Digital Library

[36]

D. Lesens, N. Halbwachs, and P. Raymond. Automatic verification of parameterized linear networks of processes. In POPL, pages 346--357, 1997.

Digital Library

[37]

B. D. Lubachevsky. An approach to automating the verification of compact parallel coordination programs i. Acta Inf., 21:125--169, 1984.

Digital Library

[38]

M. Maidl. A unifying model checking approach for safety properties of parameterized systems. In CAV, pages 311--323, 2001.

Digital Library

[39]

K. L. McMillan. Lazy abstraction with interpolants. In CAV, pages 123--136, 2006.

Digital Library

[40]

L. P. Nieto. Completeness of the Owicki-Gries system for parameterized parallel programs. In IPDPS, page 150, 2001.

Digital Library

[41]

S. Owicki and D. Gries. Verifying properties of parallel programs: an axiomatic approach. Commun. ACM, 19:279--285, May 1976. ISSN 0001-0782.

Digital Library

[42]

E. Pelz. Closure properties of deterministic petri nets. In STACS, pages 371--382, 1987.

Digital Library

[43]

A. Pnueli and E. Shahar. Liveness and acceleration in parameterized verification. In CAV, pages 328--343, 2000.

Digital Library

[44]

A. Pnueli, S. Ruah, and L. D. Zuck. Automatic deductive verification with invisible invariants. In TACAS, pages 82--97, 2001.

Digital Library

[45]

A. Pnueli, J. Xu, and L. D. Zuck. Liveness with (0, 1, 1)-counter abstraction. In CAV, pages 107--122, 2002.

Digital Library

[46]

S. Qadeer and D. Wu. Kiss: keep it simple and sequential. In PLDI, pages 14--24, 2004.

Digital Library

[47]

M. Segalov, T. Lev-Ami, R. Manevich, R. Ganesan, and M. Sagiv. Abstract transformers for thread correlation analysis. In APLAS, pages 30--46, 2009.

Digital Library

[48]

P. Wolper and B. Boigelot. Verifying systems with infinite but regular state spaces. In CAV, pages 88--97, 1998.

Digital Library

[49]

L. Zuck and A. Pnueli. Model checking and abstraction to the aid of parameterized systems (a survey). Comput. Lang. Syst. Struct., 30 (3-4):139--169, Oct. 2004.

Digital Library

Cited By

Farzan AKlumpp DPodelski A(2024)Commutativity Simplifies Proofs of Parameterized ProgramsProceedings of the ACM on Programming Languages10.1145/36329258:POPL(2485-2513)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632925
Baumann PGanardi MMajumdar RThinniyam RZetzsche G(2023)Context-Bounded Verification of Context-Free SpecificationsProceedings of the ACM on Programming Languages10.1145/35712667:POPL(2141-2170)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571266
Pani TWeissenbacher GZuleger F(2023)Thread-modular counter abstraction: automated safety and termination proofs of parameterized software by reduction to sequential program verificationFormal Methods in System Design10.1007/s10703-023-00439-664:1-3(108-145)Online publication date: 6-Oct-2023
https://doi.org/10.1007/s10703-023-00439-6
Show More Cited By

Index Terms

Proofs that count
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Correctness
2. Theory of computation
  1. Logic
    1. Proof theory
  2. Semantics and reasoning
    1. Program reasoning
      1. Program verification

Recommendations

Proofs that count
POPL '14

Counting arguments are among the most basic proof methods in mathematics. Within the field of formal verification, they are useful for reasoning about programs with infinite control, such as programs with an unbounded number of threads, or (concurrent) ...
Soter: an automatic safety verifier for erlang
AGERE! 2012: Proceedings of the 2nd edition on Programming systems, languages and applications based on actors, agents, and decentralized control abstractions

This paper presents Soter, a fully-automatic program analyser and verifier for Erlang modules. The fragment of Erlang accepted by Soter includes the higher-order functional constructs and all the key features of actor concurrency, namely, dynamic and ...
An integrated specification and verification technique for highly concurrent data structures
Abstract
We present a technique for automatically verifying safety properties of concurrent programs, in particular programs that rely on subtle dependencies of local states of different threads, such as lock-free ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2014

702 pages

ISBN:9781450325448

DOI:10.1145/2535838

General Chair:
Suresh Jagannathan
Purdue University, USA
,
Program Chair:
Peter Sewell
University of Cambridge, UK

ACM SIGPLAN Notices Volume 49, Issue 1
POPL '14
January 2014
661 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2578855
Editor:
Mark W. Bailey
Hamilton College, Clinton, NY
Issue’s Table of Contents

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGPLAN: ACM Special Interest Group on Programming Languages

In-Cooperation

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 January 2014

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

POPL '14

Sponsor:

SIGPLAN

POPL '14: The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 22 - 24, 2014

California, San Diego, USA

Acceptance Rates

POPL '14 Paper Acceptance Rate 51 of 220 submissions, 23%;

Overall Acceptance Rate 824 of 4,130 submissions, 20%

Upcoming Conference

POPL '25

Sponsor:
sigplan

The 52nd Annual ACM SIGPLAN Symposium on Principles of Programming Languages

January 19 - 25, 2025

Denver , CO , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

25
Total Citations
View Citations
491
Total Downloads

Downloads (Last 12 months)32
Downloads (Last 6 weeks)10

Reflects downloads up to 04 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Farzan AKlumpp DPodelski A(2024)Commutativity Simplifies Proofs of Parameterized ProgramsProceedings of the ACM on Programming Languages10.1145/36329258:POPL(2485-2513)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632925
Baumann PGanardi MMajumdar RThinniyam RZetzsche G(2023)Context-Bounded Verification of Context-Free SpecificationsProceedings of the ACM on Programming Languages10.1145/35712667:POPL(2141-2170)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571266
Pani TWeissenbacher GZuleger F(2023)Thread-modular counter abstraction: automated safety and termination proofs of parameterized software by reduction to sequential program verificationFormal Methods in System Design10.1007/s10703-023-00439-664:1-3(108-145)Online publication date: 6-Oct-2023
https://doi.org/10.1007/s10703-023-00439-6
Farzan AKlumpp DPodelski AJhala RDillig I(2022)Sound sequentialization for concurrent program verificationProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523727(506-521)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523727
Long TRen XWang QWang C(2022)Verifying the safety properties of distributed systems via mergeable parallelismJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2022.102646130:COnline publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1016/j.sysarc.2022.102646
Mathur UMadhusudan PViswanathan M(2020)What’s Decidable About Program Verification Modulo Axioms?Tools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45237-7_10(158-177)Online publication date: 17-Apr-2020
https://doi.org/10.1007/978-3-030-45237-7_10
Mathur UMadhusudan PViswanathan M(2019)Decidable verification of uninterpreted programsProceedings of the ACM on Programming Languages10.1145/32903593:POPL(1-29)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290359
Bakst AGleissenthall KKıcı RJhala R(2017)Verifying distributed programs via canonical sequentializationProceedings of the ACM on Programming Languages10.1145/31339341:OOPSLA(1-27)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3133934
Hoenicke JMajumdar RPodelski A(2017)Thread modularity at many levels: a pearl in compositional verificationACM SIGPLAN Notices10.1145/3093333.300989352:1(473-485)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009893
Hoenicke JMajumdar RPodelski ACastagna GGordon A(2017)Thread modularity at many levels: a pearl in compositional verificationProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009893(473-485)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009893
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents