Article

Learning boolean functions incrementally

Authors:

Bow-Yaw WangAuthors Info & Claims

CAV'12: Proceedings of the 24th international conference on Computer Aided Verification

Pages 55 - 70

https://doi.org/10.1007/978-3-642-31424-7_10

Published: 07 July 2012 Publication History

Abstract

Classical learning algorithms for Boolean functions assume that unknown targets are Boolean functions over fixed variables. The assumption precludes scenarios where indefinitely many variables are needed. It also induces unnecessary queries when many variables are redundant. Based on a classical learning algorithm for Boolean functions, we develop two learning algorithms to infer Boolean functions over enlarging sets of ordered variables. We evaluate their performance in the learning-based loop invariant generation framework.

References

[1]

Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75(2), 87-106 (1987).

Digital Library

[2]

Gheorghiu Bobaru, M., Pasareanu, C.S., Giannakopoulou, D.: Automated Assume-Guarantee Reasoning by Abstraction Refinement. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 135-148. Springer, Heidelberg (2008).

Digital Library

[3]

Bshouty, N.H.: Exact learning Boolean function via the monotone theory. Information and Computation 123(1), 146-153 (1995).

Digital Library

[4]

Chen, Y.-F., Clarke, E.M., Farzan, A., He, F., Tsai, M.-H., Tsay, Y.-K., Wang, B.-Y., Zhu, L.: Comparing Learning Algorithms in Automated Assume-Guarantee Reasoning. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010, Part I. LNCS, vol. 6415, pp. 643-657. Springer, Heidelberg (2010).

Digital Library

[5]

Chen, Y.-F., Clarke, E.M., Farzan, A., Tsai, M.-H., Tsay, Y.-K., Wang, B.-Y.: Automated Assume-Guarantee Reasoning through Implicit Learning. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 511-526. Springer, Heidelberg (2010).

Digital Library

[6]

Dutertre, B., Moura, L.D.: The Yices SMT solver. Technical report, SRI International (2006).

[7]

Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: POPL, pp. 191-202. ACM (2002).

Digital Library

[8]

Gheorghiu, M., Giannakopoulou, D., Pasareanu, C.S.: Refining Interface Alphabets for Compositional Verification. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 292-307. Springer, Heidelberg (2007).

Digital Library

[9]

Giannakopoulou, D., Pasareanu, C.S.: Special issue on learning techniques for compositional reasoning. Formal Methods in System Design 32(3), 173-174 (2008).

Digital Library

[10]

Howar, F., Steffen, B., Merten, M.: Automata Learning with Automated Alphabet Abstraction Refinement. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 263-277. Springer, Heidelberg (2011).

Digital Library

[11]

Jung, Y., Kong, S., Wang, B.-Y., Yi, K.: Deriving Invariants by Algorithmic Learning, Decision Procedures, and Predicate Abstraction. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 180-196. Springer, Heidelberg (2010).

Digital Library

[12]

Jung, Y., Lee, W., Wang, B.-Y., Yi, K.: Predicate Generation for Learning-Based Quantifier-Free Loop Invariant Inference. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 205-219. Springer, Heidelberg (2011).

Digital Library

[13]

Kearns, M.J., Vazirani, U.V.: An Introduction to Computational Learning Theory. MIT Press (1994).

Digital Library

[14]

Kong, S., Jung, Y., David, C., Wang, B.-Y., Yi, K.: Automatically Inferring Quantified Loop Invariants by Algorithmic Learning from Simple Templates. In: Ueda, K. (ed.) APLAS 2010. LNCS, vol. 6461, pp. 328-343. Springer, Heidelberg (2010).

Digital Library

[15]

Kroening, D., Strichman, O.: Decision Procedures - an algorithmic point of view. EATCS. Springer (2008).

Digital Library

[16]

Lee, W., Wang, B.Y., Yi, K.: Termination Analysis with Algorithmic Learning. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 88-104. Springer, Heidelberg (2012).

Digital Library

[17]

Saídi, H., Graf, S.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72-83. Springer, Heidelberg (1997).

Digital Library

Cited By

Cheng SJin PGuo QDu ZZhang RHu XZhao YHao YGuan XHan HZhao ZLiu XZhang XChu YMao WChen TChen YLarson K(2024)Automated CPU design by learning from input-output examplesProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/425(3843-3853)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/425
Abd Elkader KGrumberg OPăsăreanu CShoham S(2018)Automated circular assume-guarantee reasoningFormal Aspects of Computing10.1007/s00165-017-0436-030:5(571-595)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s00165-017-0436-0
Garg PNeider DMadhusudan PRoth D(2016)Learning invariants using decision trees and implication counterexamplesACM SIGPLAN Notices10.1145/2914770.283766451:1(499-512)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2914770.2837664
Show More Cited By

Recommendations

On the Symmetric Negabent Boolean Functions
INDOCRYPT '09: Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology

We study the negabent Boolean functions which are symmetric. The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called a negabent function. For a bent function, the absolute spectral values are the same ...
Boolean functions with two distinct Walsh coefficients

Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions__ __ This paper proves that all Boolean functions with exactly two distinct Walsh coefficients ...
Look into the Mirror: Evolving Self-dual Bent Boolean Functions
Genetic Programming
Abstract
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions, even ...

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

CAV'12: Proceedings of the 24th international conference on Computer Aided Verification

July 2012

789 pages

ISBN:9783642314230

Editors:
P. Madhusudan
Dept. of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL
,
Sanjit A. Seshia
Dept. of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA

Sponsors

NEC Labs: NEC Labs
IBMR: IBM Research
Intel: Intel
Microsoft Research: Microsoft Research

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 July 2012

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 29 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Cheng SJin PGuo QDu ZZhang RHu XZhao YHao YGuan XHan HZhao ZLiu XZhang XChu YMao WChen TChen YLarson K(2024)Automated CPU design by learning from input-output examplesProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/425(3843-3853)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/425
Abd Elkader KGrumberg OPăsăreanu CShoham S(2018)Automated circular assume-guarantee reasoningFormal Aspects of Computing10.1007/s00165-017-0436-030:5(571-595)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s00165-017-0436-0
Garg PNeider DMadhusudan PRoth D(2016)Learning invariants using decision trees and implication counterexamplesACM SIGPLAN Notices10.1145/2914770.283766451:1(499-512)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2914770.2837664
Garg PNeider DMadhusudan PRoth DBodik RMajumdar R(2016)Learning invariants using decision trees and implication counterexamplesProceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2837614.2837664(499-512)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2837614.2837664
He FWang BYin LZhu LJalote PBriand LHoek A(2014)Symbolic assume-guarantee reasoning through BDD learningProceedings of the 36th International Conference on Software Engineering10.1145/2568225.2568253(1071-1082)Online publication date: 31-May-2014
https://dl.acm.org/doi/10.1145/2568225.2568253
Garg PLöding CMadhusudan PNeider D(2013)LearningźUniversallyźQuantifiedźInvariants of LinearźDataźStructuresProceedings of the 25th International Conference on Computer Aided Verification - Volume 804410.5555/2958031.2958058(813-829)Online publication date: 13-Jul-2013
https://dl.acm.org/doi/10.5555/2958031.2958058
Chen YWang B(2013)BULLProceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-642-36742-7_38(537-542)Online publication date: 16-Mar-2013
https://dl.acm.org/doi/10.1007/978-3-642-36742-7_38
Lee WWang BYi K(2012)Termination analysis with algorithmic learningProceedings of the 24th international conference on Computer Aided Verification10.1007/978-3-642-31424-7_12(88-104)Online publication date: 7-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31424-7_12

View Options

View options

Figures

Tables

Media

View Table of Conten