research-article

Analyzing recursive programs using a fixed-point calculus

Authors:

Salvatore La Torre,

Madhusudan Parthasarathy,

Gennaro ParlatoAuthors Info & Claims

ACM SIGPLAN Notices, Volume 44, Issue 6

Pages 211 - 222

https://doi.org/10.1145/1543135.1542500

Published: 15 June 2009 Publication History

Abstract

We show that recursive programs where variables range over finite domains can be effectively and efficiently analyzed by describing the analysis algorithm using a formula in a fixed-point calculus. In contrast with programming in traditional languages, a fixed-point calculus serves as a high-level programming language to easily, correctly, and succinctly describe model-checking algorithms While there have been declarative high-level formalisms that have been proposed earlier for analysis problems (e.g., Datalog the fixed-point calculus we propose has the salient feature that it also allows algorithmic aspects to be specified.

We exhibit two classes of algorithms of symbolic (BDD-based) algorithms written using this framework-- one for checking for errors in sequential recursive Boolean programs, and the other to check for errors reachable within a bounded number of context-switches in a concurrent recursive Boolean program. Our formalization of these otherwise complex algorithms is extremely simple, and spans just a page of fixed-point formulae. Moreover, we implement these algorithms in a tool called Getafix which expresses algorithms as fixed-point formulae and evaluates them efficiently using a symbolic fixed-point solver called Mucke. The resulting model-checking tools are surprisingly efficient and are competitive in performance with mature existing tools that have been fine-tuned for these problems.

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Cited By

Inverso OTomasco EFischer BLa Torre SParlato G(2021)Bounded Verification of Multi-threaded Programs via Lazy SequentializationACM Transactions on Programming Languages and Systems10.1145/347853644:1(1-50)Online publication date: 9-Dec-2021
https://dl.acm.org/doi/10.1145/3478536
Johnson AWahl T(2021)Delay-Bounded Scheduling Without Delay!Computer Aided Verification10.1007/978-3-030-81685-8_18(380-402)Online publication date: 15-Jul-2021
https://doi.org/10.1007/978-3-030-81685-8_18
Akshay SGastin PKrishna SRoychowdhury S(2020)Revisiting Underapproximate Reachability for Multipushdown SystemsTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45190-5_21(387-404)Online publication date: 17-Apr-2020
https://doi.org/10.1007/978-3-030-45190-5_21
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Analyzing recursive programs using a fixed-point calculus

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 44, Issue 6

PLDI '09

June 2009

478 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1543135

Issue’s Table of Contents

PLDI '09: Proceedings of the 30th ACM SIGPLAN Conference on Programming Language Design and Implementation
June 2009
492 pages
ISBN:9781605583921
DOI:10.1145/1542476
General Chair:
Michael Hind
IBM Research, USA
,
Program Chair:
Amer Diwan
University of Colorado at Boulder, USA

Copyright © 2009 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 June 2009

Published in SIGPLAN Volume 44, Issue 6

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Cited By

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https://dl.acm.org/doi/10.1145/3478536
Johnson AWahl T(2021)Delay-Bounded Scheduling Without Delay!Computer Aided Verification10.1007/978-3-030-81685-8_18(380-402)Online publication date: 15-Jul-2021
https://doi.org/10.1007/978-3-030-81685-8_18
Akshay SGastin PKrishna SRoychowdhury S(2020)Revisiting Underapproximate Reachability for Multipushdown SystemsTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-45190-5_21(387-404)Online publication date: 17-Apr-2020
https://doi.org/10.1007/978-3-030-45190-5_21
Liu PWahl TLal A(2019)Verifying Asynchronous Event-Driven Programs Using Partial Abstract TransformersComputer Aided Verification10.1007/978-3-030-25543-5_22(386-404)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-25543-5_22
Atig MBouajjani AParlato G(2014)Context-Bounded Analysis of TSO SystemsFrom Programs to Systems. The Systems perspective in Computing10.1007/978-3-642-54848-2_2(21-38)Online publication date: 2014
https://doi.org/10.1007/978-3-642-54848-2_2
Inverso OTomasco EFischer BLa Torre SParlato G(2014)Bounded Model Checking of Multi-threaded C Programs via Lazy SequentializationProceedings of the 16th International Conference on Computer Aided Verification - Volume 855910.1007/978-3-319-08867-9_39(585-602)Online publication date: 18-Jul-2014
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Hague MLin A(2012)Synchronisation- and reversal-bounded analysis of multithreaded programs with countersProceedings of the 24th international conference on Computer Aided Verification10.1007/978-3-642-31424-7_22(260-276)Online publication date: 7-Jul-2012
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Bouajjani A(2024)On Verifying Concurrent Programs Under Weak Consistency Models: Decidability and ComplexityTaming the Infinities of Concurrency10.1007/978-3-031-56222-8_7(133-147)Online publication date: 20-Mar-2024
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