Advertisement

An Axiomatization for Cylinder Computation Model

  • Nan Zhang
  • Zhenhua Duan
  • Cong Tian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)

Abstract

To model and verify multi-core parallel programs, the paper proposes an axiom system for Propositional Projection Temporal Logic with Cylinder Computation Model (CCM-PPTL). To do so, the syntax and semantics of CCM-PPTL are presented. Further, based on the logical laws of PPTL, some algebraic laws of sequence expressions and logical laws regarding CCM operators are proved. Moreover, the axiom system of CCM-PPTL is established by extending that of PPTL with some axioms and inference rules of CCM operators. In addition, the soundness and completeness of the system are proved.

Keywords

Axiom System Multi-core Parallel Formal Method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development, Heidelberg (2004)Google Scholar
  2. 2.
    Brock, B., Kaufmann, M., Moore, J.: ACL2 theorems about commercial micro-processors. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 275–293. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  3. 3.
    Duan, Z.: Temporal Logic and Temporal Logic Programming. Science Press, Beijing (2006)Google Scholar
  4. 4.
    Duan, Z., Tian, C., Zhang, L.: A decision procedure for propositional projection temporal logic with infinite models. Acta Informatica 45, 43–78 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Duan, Z., Tian, C.: A unified model checking approach with projection temporal logic. In: Liu, S., Araki, K., Maibaum, T. (eds.) ICFEM 2008. LNCS, vol. 5256, pp. 167–186. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Duan, Z., Zhang, N., Koutny, M.: A complete proof system for propositional projection temporal logic. Theoretical Computer Science 497, 84–107 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Duan, Z., Tian, C.: A practical decision procedure for propositional projection temporal logic with infinite models. Theoretical Computer Science (2014) doi:10.1016/j.tcs.2014.02.011Google Scholar
  8. 8.
    Gordon, M., Melham, T.: Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press (1993)Google Scholar
  9. 9.
    Holzmann, G.: The model checker SPIN. IEEE Trans. Softw. Eng. 23(5), 279–295 (1997)CrossRefMathSciNetGoogle Scholar
  10. 10.
    McMillan, K.: Symbolic Model Checking: An Approach to the State Explosion Problem, Dordrecht (1993)Google Scholar
  11. 11.
    Owre, S., Rushby, J., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS (LNAI), vol. 607, pp. 748–752. Springer, Heidelberg (1992)Google Scholar
  12. 12.
    Paulson, L.C.: Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)CrossRefzbMATHGoogle Scholar
  13. 13.
    Sistla, A.: Theoretical issues in the design and verification of distributed systems, Ph.D. Thesis. Harvard University (1983)Google Scholar
  14. 14.
    Tian, C., Duan, Z.: Expressiveness of propositional projection temporal logic with star. Theoretical Computer Science 412(18), 1729–1744 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Vardi, M.: A temporal fixpoint calculus. In: POPL 1988, pp. 250–259 (1988)Google Scholar
  16. 16.
    Wolper, P.: Temporal logic can be more expressive. Information and Control 56, 72–99 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Zhang, N., Duan, Z., Tian, C.: A cylinder computation model for many-core parallel computing. Theoretical Computer Science 497, 68–83 (2013)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nan Zhang
    • 1
  • Zhenhua Duan
    • 1
  • Cong Tian
    • 1
  1. 1.Institute of Computing Theory and Technology, and ISN LaboratoryXidian UniversityXi’anChina

Personalised recommendations