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Automatically inferring loop invariants via algorithmic learning†

Published online by Cambridge University Press:  17 December 2014

YUNGBUM JUNG ,
SOONHO KONG ,
CRISTINA DAVID ,
BOW-YAW WANG  and
KWANGKEUN YI
YUNGBUM JUNG
Affiliation:
Program Analysis Department, Fasoo, Seoul, Republic of Korea
SOONHO KONG
Affiliation:
School of Computer Science, Carnegie Mellon University, Pittsburgh, United States Email: soonhok@cs.cmu.edu
CRISTINA DAVID
Affiliation:
Department of Computer Science School of Computing, National University of Singapore, Singapore
BOW-YAW WANG
Affiliation:
INRIA and Institute of Information Science, Academia Sinica, Taipei, Taiwan
KWANGKEUN YI
Affiliation:
School of Computer Science and Engineering, Seoul National University, Seoul, Republic of Korea
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Abstract

By combining algorithmic learning, decision procedures, predicate abstraction and simple templates for quantified formulae, we present an automated technique for finding loop invariants. Theoretically, this technique can find arbitrary first-order invariants (modulo a fixed set of atomic propositions and an underlying satisfiability modulo theories solver) in the form of the given template and exploit the flexibility in invariants by a simple randomized mechanism. In our study, the proposed technique was able to find quantified invariants for loops from the Linux source and other realistic programs. Our contribution is a simpler technique than the previous works yet with a reasonable derivation power.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 4: APLAS 2010 , May 2015 , pp. 892 - 915
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

This work was supported by the Engineering Research Center of Excellence Program of Korea Ministry of Education, Science and Technology (MEST) / National Research Foundation of Korea (NRF) (Grant 2011-0000971), the National Science Foundation (award no. CNS0926181), the National Science Council of Taiwan projects No. NSC97-2221-E-001-003-MY3, NSC97-2221-E-001-006-MY3, the FORMES Project within LIAMA Consortium, and the French ANR project SIVES ANR-08-BLAN-0326-01. This research was sponsored in part by the National Science Foundation (award no. CNS0926181) and by Republic of Korea Dual Use Program Cooperation Center (DUPC) of Agency for Defense Development (ADD).

References

Alur, R., Cerný, P., Madhusudan, P. and Nam, W. (2005a) Synthesis of interface specifications for java classes. In: POPL, ACM 98–109.Google Scholar
Alur, R., Madhusudan, P. and Nam, W. (2005b) Symbolic compositional verification by learning assumptions. In: CAV. Springer Lecture Notes in Computer Science 3576 548–562.CrossRefGoogle Scholar
Bertot, Y. and Castéran, P. (2004) Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science, Springer Verlag.CrossRefGoogle Scholar
Bshouty, N. H. (1995) Exact learning boolean functions via the monotone theory. Information and Computation 123 146–153.Google Scholar
Chen, Y.-F., Farzan, A., Clarke, E. M., Tsay, Y.-K. and Wang, B.-Y. (2009) Learning minimal separating DFA's for compositional verification. In: TACAS. Springer Lecture Notes in Computer Science 5505 31–45.CrossRefGoogle Scholar
Cobleigh, J. M., Giannakopoulou, D. and Păsăreanu, C. S. (2003) Learning assumptions for compositional verification. In: TACAS. Springer Lecture Notes in Computer Science 2619 331–346.Google Scholar
Dutetre, B. and de Moura, L. D. (2006) The Yices SMT solver, Technical report, SRI International. Available at: http://yices.csl.sri.com/tool-paper.pdfGoogle Scholar
Flanagan, C. and Qadeer, S. (2002) Predicate abstraction for software verification. In: POPL, ACM 191–202.Google Scholar
Ge, Y. and Moura, L. (2009) Complete instantiation for quantified formulas in satisfiabiliby modulo theories. In: CAV. Springer-Verlag Lecture Notes in Computer Science 5643 306–320.Google Scholar
Gulwani, S., McCloskey, B. and Tiwari, A. (2008a) Lifting abstract interpreters to quantified logical domains. In: POPL, ACM 235–246.Google Scholar
Gulwani, S., Srivastava, S. and Venkatesan, R. (2008b) Program analysis as constraint solving. In: PLDI, ACM 281–292.Google Scholar
Gulwani, S., Srivastava, S. and Venkatesan, R. (2009) Constraint-based invariant inference over predicate abstraction. In: VMCAI. Springer Lecture Notes in Computer Science 5403 120–135.Google Scholar
Gupta, A., McMillan, K. L. and Fu, Z. (2007) Automated assumption generation for compositional verification. In: CAV. Springer Lecture Notes in Computer Science 4590 420–432.Google Scholar
Gupta, A. and Rybalchenko, A. (2009) Invgen: An efficient invariant generator. In: CAV. Springer Lecture Notes in Computer Science 5643 634–640.CrossRefGoogle Scholar
Halbwachs, N. and Péron, M. (2008) Discovering properties about arrays in simple programs. In: PLDI 339–348.Google Scholar
Henzinger, T. A., Hottelier, T., Kovács, L. and Voronkov, A. (2010) Invariant and type inference for matrices. In: VMCAI 163–179.Google Scholar
Jhala, R. and McMillan, K. L. (2007) Array abstractions from proofs. In: CAV. Springer Lecture Notes in Computer Science 4590 193–206.CrossRefGoogle Scholar
Jung, Y., Kong, S., Wang, B.-Y. and Yi, K. (2010) Deriving invariants in propositional logic by algorithmic learning, decision procedure and predicate abstraction. In: VMCAI. Springer Lecture Notes in Computer Science 5944 180–196.CrossRefGoogle Scholar
Jung, Y., Lee, W., Wang, B.-Y. and Yi, K. (2011) Predicate generation for learning-based quantifier-free loop invariant inference. In: TACAS 205–219.Google Scholar
Kong, S., Jung, Y., David, C., Wang, B.-Y. and Yi, K. (2010) Automatically inferring quantified loop invariants by algorithmic learning from simple templates. In: The 8th ASIAN Symposium on Programming Languages and Systems (APLAS'10) 328–343.Google Scholar
Kovács, L. and Voronkov, A. (2009) Finding loop invariants for programs over arrays using a theorem prover. In: FASE. Springer Lecture Notes in Computer Science 5503 470–485.Google Scholar
Kroening, D. and Strichman, O. (2008) Decision Procedures An Algorithmic Point of View, EATCS, Springer.Google Scholar
Lahiri, S. K., Bryant, R. E. and Bryant, A. E. (2004) Constructing quantified invariants via predicate abstraction. In: VMCAI. Springer Lecture Notes in Computer Science 2937 267–281.Google Scholar
McMillan, K. L. (2008) Quantified invariant generation using an interpolating saturation prover. In: TACAS. Springer Lecture Notes in Computer Science 4693 413–427.CrossRefGoogle Scholar
Nipkow, T., Paulson, L. C. and Wenzel, M. (2002) Isabelle/HOL — A Proof Assistant for Higher-Order Logic, Lecture Notes in Computer Science, volume 2283.Google Scholar
Srivastava, S. and Gulwani, S. (2009) Program verification using templates over predicate abstraction. In: PLDI, ACM 223–234.Google Scholar
Srivastava, S., Gulwani, S. and Foster, J. S. (2009) Vs3: Smt solvers for program verification. In: CAV '09: Proceedings of Computer Aided Verification 702–708.Google Scholar