Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

The Octahedron Abstract Domain

  • Conference paper
Static Analysis (SAS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3148))

Included in the following conference series:

Abstract

An interesting area in static analysis is the study of numeric properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numeric abstract domain called octahedron that represents constraints of the form (± x j ± ... ± x k c), where x i are numerical variables such that x i ≥ 0. The implementation of octahedra is based on a new kind of decision diagrams called Octahedron Decision Diagrams (OhDD).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Behrmann, G., Larsen, K.G., Pearson, J., Weise, C., Yi, W.: Efficient timed reachability analysis using clock difference diagrams. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 341–353. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  4. Clarisó, R., Cortadella, J.: Verification of timed circuits with symbolic delays. In: Proc. of Asia and South Pacific Design Automation Conference, pp. 628–633 (2004)

    Google Scholar 

  5. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc. of the ACM Symposium on Principles of Programming Languages, pp. 238–252. ACM Press, New York (1977)

    Google Scholar 

  6. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proc. of the ACM Symposium on Principles of Programming Languages, pp. 84–97. ACM Press, New York (1978)

    Chapter  Google Scholar 

  7. Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)

    Google Scholar 

  8. Dor, N., Rodeh, M., Sagiv, M.: CSSV: towards a realistic tool for statically detecting all buffer overflows in C. In: Proceedings of the ACM SIGPLAN 2003 conference on Programming lan guage design and implementation, pp. 155–167. ACM Press, New York (2003)

    Chapter  Google Scholar 

  9. Asarin, E., Bozga, M., Kerbrat, A., Maler, O., Pnueli, M., Rasse, A.: Data structures for the verification of timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 346–360. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  10. Fujita, M., McGeer, P.C., Yang, J.C.-Y.: Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Formal Methods in System Design 10(2/3), 149–169 (1997)

    Article  Google Scholar 

  11. Halbwachs, N., Proy, Y.-E., Roumanoff, P.: Verification of real-time systems using linear relation analysis. Formal Methods in System Design 11(2), 157–185 (1997)

    Article  Google Scholar 

  12. Henzinger, T.A.: The Temporal Specification and Verification of Real-Time Systems. PhD thesis, Stanford University (August 1991)

    Google Scholar 

  13. Mauras, C.: Symbolic simulation of interpreted automata. In: 3rd Workshop on Synchronous Programming (December 1996)

    Google Scholar 

  14. Minato, S.: Zero-supressed BDDs for set manipulation in combinatorial problems. In: Proc. ACM/IEEE Design Automation Conference, pp. 272–277 (1993)

    Google Scholar 

  15. Miné, A.: A new numerical abstract domain based on difference-bound matrices. In: Danvy, O., Filinski, A. (eds.) PADO 2001. LNCS, vol. 2053, pp. 155–172. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Miné, A.: The octagon abstract domain. In: Analysis, Slicing and Tranformation (in Working Conference on Reverse Engineering), October 2001, pp. 310–319. IEEE CS Press, Los Alamitos (2001)

    Google Scholar 

  17. Møller, J., Lichtenberg, J., Andersen, H.R., Hulgaard, H.: Difference decision diagrams. In: Computer Science Logic, The IT University of Copenhagen, Denmark (1999)

    Google Scholar 

  18. Murata, T.: State equation, controllability and maximal matchings of Petri nets. IEEE Transactions on Automatic Control  AC-22(3), 412–416 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  19. New Polka: Convex Polyhedra Library, http://www.irisa.fr/prive/bjeannet/newpolka.html

  20. Piguet, C., et al.: Memory element of the Master-Slave latch type, constructed by CMOS technology. US Patent 5,748,522 (1998)

    Google Scholar 

  21. Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proc. International Conf. Computer-Aided Design (ICCAD), pp. 42–47 (1993)

    Google Scholar 

  22. Simon, A., King, A., Howe, J.M.: Two Variables per Linear Inequality as an Abstract Domain. In: Leuschel, M. (ed.) LOPSTR 2002. LNCS, vol. 2664, pp. 71–89. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  23. Somenzi, F.: CUDD: Colorado university decision diagram package, Available online at http://vlsi.colorado.edu/~fabio/CUDD

  24. Wang, F.: Symbolic parametric safety analysis of linear hybrid systems with BDD-like datastructures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 295–307. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Clarisó, R., Cortadella, J. (2004). The Octahedron Abstract Domain. In: Giacobazzi, R. (eds) Static Analysis. SAS 2004. Lecture Notes in Computer Science, vol 3148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27864-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27864-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22791-5

  • Online ISBN: 978-3-540-27864-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics