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Using Datalog with Binary Decision Diagrams for Program Analysis

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3780)

Abstract

Many problems in program analysis can be expressed naturally and concisely in a declarative language like Datalog. This makes it easy to specify new analyses or extend or compose existing analyses. However, previous implementations of declarative languages perform poorly compared with traditional implementations. This paper describes bddbddb, a BDD-Based Deductive DataBase, which implements the declarative language Datalog with stratified negation, totally-ordered finite domains and comparison operators. bddbddb uses binary decision diagrams (BDDs) to efficiently represent large relations. BDD operations take time proportional to the size of the data structure, not the number of tuples in a relation, which leads to fast execution times. bddbddb is an effective tool for implementing a large class of program analyses. We show that a context-insensitive points-to analysis implemented with bddbddb is about twice as fast as a carefully hand-tuned version. The use of BDDs also allows us to solve heretofore unsolved problems, like context-sensitive pointer analysis for large programs.

Keywords

  • Boolean Function
  • Logic Program
  • Logic Programming
  • Intermediate Representation
  • Binary Decision Diagram

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Avots, D., Dalton, M., Livshits, V.B., Lam, M.S.: Improving software security with a C pointer analysis. In: ICSE 2005: Proceedings of the 27th International Conference on Software Engineering. ACM Press, New York (2005)

    Google Scholar 

  2. Ball, T., Rajamani, S.K.: Bebop: A symbolic model checker for boolean programs. In: Proceedings of the 7th International SPIN Workshop on SPIN Model Checking and Software Verification, pp. 113–130. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  3. Ball, T., Rajamani, S.K.: Automatically validating temporal safety properties of interfaces. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 103–122. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  4. Bancilhon, F., Maier, D., Sagiv, Y., Ullman, J.D.: Magic sets and other strange ways to implement logic programs (extended abstract). In: PODS 1986: Proceedings of the Fifth ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 1–15. ACM Press, New York (1986)

    CrossRef  Google Scholar 

  5. Berndl, M., Lhoták, O., Qian, F., Hendren, L., Umanee, N.: Points-to analysis using BDDs. In: PLDI 2003: Proceedings of the ACM SIGPLAN 2003 Conference on Programming Language Design and Implementation, pp. 103–114. ACM Press, New York (2003)

    CrossRef  Google Scholar 

  6. Besson, F., Jensen, T.: Modular class analysis with datalog. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 19–36. Springer, Heidelberg (2003), http://www.irisa.fr/lande/fbesson/fbesson.html

    CrossRef  Google Scholar 

  7. Beyer, D., Noack, A., Lewerentz, C.: Simple and efficient relational querying of software structures. In: Proceedings of the 10th IEEE Working Conference on Reverse Engineering (November 2003)

    Google Scholar 

  8. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 35(8), 677–691 (1986)

    MATH  CrossRef  Google Scholar 

  9. Carbin, M., Whaley, J., Lam, M.S.: Finding effective variable orderings for BDD-based program analysis (2005) (To be submitted for publication)

    Google Scholar 

  10. Ceri, S., Gottlob, G., Tanca, L.: Logic programming and databases. Springer, New York (1990)

    Google Scholar 

  11. Chandra, A., Harel, D.: Horn clauses and generalizations. Journal of Logic Programming 2(1), 1–15 (1985)

    MATH  CrossRef  MathSciNet  Google Scholar 

  12. Chen, W., Warren, D.S.: Tabled evaluation with delaying for general logic programs. J. ACM 43(1), 20–74 (1996)

    MATH  CrossRef  MathSciNet  Google Scholar 

  13. Corsini, M.-M., Musumbu, K., Rauzy, A., Charlier, B.L.: Efficient bottom-up abstract interpretation of prolog by means of constraint solving over symbolic finite domains. In: Penjam, J., Bruynooghe, M. (eds.) PLILP 1993. LNCS, vol. 714, pp. 75–91. Springer, Heidelberg (1993)

    Google Scholar 

  14. Dawson, S., Ramakrishnan, C.R., Warren, D.S.: Practical program analysis using general purpose logic programming systemsa case study. In: PLDI 1996: Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language Design and Implementation, pp. 117–126. ACM Press, New York (1996)

    CrossRef  Google Scholar 

  15. Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 619–649 (1991)

    CrossRef  Google Scholar 

  16. Halevy, A.Y., Mumick, I.S., Sagiv, Y., Shmueli, O.: Static analysis in datalog extensions. J. ACM 48(5), 971–1012 (2001)

    CrossRef  MathSciNet  Google Scholar 

  17. Iwaihara, M., Inoue, Y.: Bottom-up evaluation of logic programs using binary decision diagrams. In: ICDE 1995: Proceedings of the Eleventh International Conference on Data Engineering, pp. 467–474. IEEE Computer Society, Los Alamitos (1995)

    CrossRef  Google Scholar 

  18. Lam, M.S., Whaley, J., Livshits, V.B., Martin, M.C., Avots, D., Carbin, M., Unkel, C.: Context-sensitive program analysis as database queries. In: Proceedings of the Twenty-fourth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 2005. ACM, New York (2005)

    Google Scholar 

  19. Lhoták, O., Hendren, L.: Jedd: a BDD-based relational extension of Java. In: PLDI 2004: Proceedings of the ACM SIGPLAN 2004 Conference on Programming Language Design and Implementation, pp. 158–169. ACM Press, New York (2004)

    CrossRef  Google Scholar 

  20. Lind-Nielsen, J.: BuDDy, a binary decision diagram package, http://buddy.sourceforge.net

  21. Liu, Y.A., Stoller, S.D.: From datalog rules to efficient programs with time and space guarantees. In: PPDP 2003: Proceedings of the 5th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming, pp. 172–183. ACM Press, New York (2003)

    CrossRef  Google Scholar 

  22. Livshits, V.B., Lam, M.S.: Finding security vulnerabilities in java applications with static analysis. In: 14th USENIX Security Symposium, August 2005. USENIX (2005)

    Google Scholar 

  23. Martin, M.C., Livshits, V.B., Lam, M.S.: Finding application errors using PQL: a program query language. In: Proceedings of the ACM Conference on Object-Oriented Programming, Systems, Languages, and Applications (OOPSLA) (October 2005)

    Google Scholar 

  24. Naughton, J.F., Ramakrishnan, R.: Bottom-up evaluation of logic programs. In: Computational Logic - Essays in Honor of Alan Robinson, pp. 640–700 (1991)

    Google Scholar 

  25. Naughton, J.F., Ramakrishnan, R., Sagiv, Y., Ullman, J.D.: Efficient evaluation of right-, left-, and multi-linear rules. In: SIGMOD 1989: Proceedings of the 1989 ACM SIGMOD International Conference on Management of Data, pp. 235–242. ACM Press, New York (1989)

    CrossRef  Google Scholar 

  26. Ramakrishnan, R., Srivastava, D., Sudarshan, S.: Rule ordering in bottom-up fixpoint evaluation of logic programs. In: Proceedings of the 16th International Conference on Very Large Data Bases, pp. 359–371. Morgan Kaufmann Publishers Inc., San Francisco (1990)

    Google Scholar 

  27. Ramakrishnan, R., Ullman, J.D.: A survey of research on deductive database systems. J. Logic Programming 23(2), 125–149 (1993)

    CrossRef  MathSciNet  Google Scholar 

  28. Ramalingam, G.: Identifying loops in almost linear time. ACM Transactions on Programming Languages and Systems 21(2), 175–188 (1999)

    CrossRef  MathSciNet  Google Scholar 

  29. Reps, T.W.: Demand Interprocedural Program Analysis Using Logic Databases, pp. 163–196. Kluwer, Dordrecht (1994)

    Google Scholar 

  30. Sagiv, Y.: Optimizing datalog programs. In: PODS 1987: Proceedings of the Sixth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 349–362. ACM Press, New York (1987)

    CrossRef  Google Scholar 

  31. Sagonas, K., Swift, T., Warren, D.S.: Xsb as an efficient deductive database engine. In: SIGMOD 1994: Proceedings of the 1994 ACM SIGMOD International Conference on Management of Data, pp. 442–453. ACM Press, New York (1994)

    CrossRef  Google Scholar 

  32. Sittampalam, G., de Moor, O., Larsen, K.F.: Incremental execution of transformation specifications. In: POPL 2004: Proceedings of the 31st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 26–38. ACM Press, New York (2004)

    CrossRef  Google Scholar 

  33. Tamaki, H., Sato, T.: Old resolution with tabulation. In: Proceedings on Third International Conference on Logic Programming, pp. 84–98. Springer, New York (1986)

    Google Scholar 

  34. Tarjan, R.E.: Testing flow graph reducibility. Journal of Computer and System Sciences 9(3), 355–365 (1974)

    MATH  MathSciNet  CrossRef  Google Scholar 

  35. Ullman, J.D.: Bottom-up beats top-down for datalog. In: PODS 1989: Proceedings of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 140–149. ACM Press, New York (1989)

    CrossRef  Google Scholar 

  36. Ullman, J.D.: Principles of Database and Knowledge-Base Systems, 2nd edn. Computer Science Press, Rockville (1989)

    Google Scholar 

  37. Whaley, J.: JavaBDD library, http://javabdd.sourceforge.net

  38. Whaley, J., Lam, M.S.: Cloning-based context-sensitive pointer alias analysis using binary decision diagrams. In: PLDI 2004: Proceedings of the ACM SIGPLAN 2004 Conference on Programming Language Design and Implementation, pp. 131–144. ACM Press, New York (2004)

    CrossRef  Google Scholar 

  39. Zhou, N.-F., Sato, T.: Efficient fixpoint computation in linear tabling. In: PPDP 2003: Proceedings of the 5th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming, pp. 275–283. ACM Press, New York (2003)

    CrossRef  Google Scholar 

  40. Zhu, J.: Symbolic pointer analysis. In: ICCAD 2002: Proceedings of the 2002 IEEE/ACM International Conference on Computer-Aided Design, pp. 150–157. ACM Press, New York (2002)

    CrossRef  Google Scholar 

  41. Zhu, J., Calman, S.: Symbolic pointer analysis revisited. In: PLDI 2004: Proceedings of the ACM SIGPLAN 2004 Conference on Programming Language Design and Implementation, pp. 145–157. ACM Press, New York (2004)

    CrossRef  Google Scholar 

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Whaley, J., Avots, D., Carbin, M., Lam, M.S. (2005). Using Datalog with Binary Decision Diagrams for Program Analysis. In: Yi, K. (eds) Programming Languages and Systems. APLAS 2005. Lecture Notes in Computer Science, vol 3780. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11575467_8

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  • DOI: https://doi.org/10.1007/11575467_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29735-2

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