Structural Contradictions

  • Cindy Eisner
  • Dana Fisman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5394)


We study the relation between logical contradictions such as p ∧ ¬p and structural contradictions such as p ∩ (p.q). Intuitively, we expect the two to be treated similarly, but they are not by PSL, nor by SVA. We provide a solution that treats both kinds of contradictions in a consistent manner. The solution reveals that not all structural contradictions are created equal: we must distinguish between them in order to preserve important characteristics of the logic. A happy result of our solution is that it provides the semantics over the natural alphabet 2 P , as opposed to the current semantics of PSL/SVA that use an inflated alphabet including the cryptic letters ⊤ and \(\bot\). We show that the complexity of model checking PSL/SVA is not affected by our proposed semantics.


Model Check Atomic Proposition Propositional Formula Empty Word Strong View 
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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  1. 1.
    Accellera Property Specification Language Reference Manual Version 1.0 (January 2003)Google Scholar
  2. 2.
    Accellera Property Specification Language Reference Manual Version 1.1 (June 2004)Google Scholar
  3. 3.
    Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distributed Computing 2(3), 117–126 (1987)CrossRefzbMATHGoogle Scholar
  4. 4.
    Armoni, R., Bustan, D., Kupferman, O., Vardi, M.Y.: Resets vs. aborts in linear temporal logic. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 65–80. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Ben-David, S., Bloem, R., Fisman, D., Griesmayer, A., Pill, I., Ruah, S.: Automata construction algorithms optimized for PSL (Deliverable 3.2/4). Technical report, Prosyd (2005)Google Scholar
  6. 6.
    Bustan, D., Fisman, D., Havlicek, J.: Automata construction for PSL. Technical Report MCS05-04, The Weizmann Institute of Science (May 2005)Google Scholar
  7. 7.
    Bustan, D., Havlicek, J.: Some complexity results for SystemVerilog assertions. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 205–218. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Eisner, C., Fisman, D.: A Practical Introduction to PSL. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    Eisner, C., Fisman, D., Havlicek, J.: A topological characterization of weakness. In: Proc. PODC 2005, pp. 1–8. ACM Press, New York (2005)Google Scholar
  10. 10.
    Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout, D.: Reasoning with temporal logic on truncated paths. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Eisner, C., Fisman, D., Havlicek, J., Mårtensson, J.: The ⊤,\(\bot\) approach to truncated semantics. Technical Report 2006.01, Accellera (May 2006)Google Scholar
  12. 12.
    Eisner, C., Fisman, D., Havlicek, J., McIsaac, A., Van Campenhout, D.: The definition of a temporal clock operator. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 857–870. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fisman, D.: On the characterization of until as a fixed point under clocked semantics. In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 19–33. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  16. 16.
    Harel, D., Sherman, R.: Looping vs. repeating in dynamic logic. Information and Control 55, 175–192 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    IEEE Standard for Property Specification Language (PSL). IEEE Std 1850TM-2005, Annex B (2005)Google Scholar
  18. 18.
    IEEE Standard for SystemVerilog – Unified Hardware Design, Specification, and Verification Language. IEEE Std 1800TM-2005, Annex E (2005)Google Scholar
  19. 19.
    Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, New York (1995)CrossRefzbMATHGoogle Scholar
  20. 20.
    Pnueli, A.: The temporal logic of concurrent programs. Theoretical Computer Science 13, 45–60 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Information and Computation 115(1), 1–37 (1994)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cindy Eisner
    • 1
  • Dana Fisman
    • 1
    • 2
  1. 1.IBM Haifa Research LaboratoryIsrael
  2. 2.Hebrew UniversityIsrael

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