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On Complexity of Grammars Related to the Safety Problem

  • Tomasz Jurdziński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)

Abstract

Leftist grammars were introduced by Motwani et. al., who established the relationship between the complexity of accessibility problem (or safety problem) for certain general protection system and the membership problem of these grammars. The membership problem for leftist grammars is decidable. This implies the decidability of the accessibility problem. It is shown that the membership problem for leftist grammars is PSPACE-hard. Therefore, the accessibility problem in the appropriate protection systems is PSPACE-hard as well. Furthermore, the PSPACE-hardness result is adopted to very restricted class of leftist grammars, if the grammar is a part of the input.

Keywords

Protection System Production Rule Trust Management Safety Problem Derivation Step 
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. 1.
    Bandyopadhyay, S., Mahajan, M., Kumar, K.N.: A non-regular leftist language. Manuscript (2005)Google Scholar
  2. 2.
    Blaze, M., Feigenbaum, J., Ioannidis, J., Keromytis, A.: The role of trust management in distributed security. In: Vitek, J. (ed.) Secure Internet Programming. LNCS, vol. 1603, pp. 185–210. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Budd, T.: Safety in grammatical protection systems. International Journal of Computer and Information Sciences 12(6), 413–430 (1983)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cheiner, O., Saraswat, V.: Security Analysis of Matrix. Technical report, AT&T Shannon Laboratory (1999)Google Scholar
  5. 5.
    Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)MATHGoogle Scholar
  6. 6.
    Harrison, M., Ruzzo, W., Ullman, J.: Protection in operating systems. Communications of the ACM 19(8), 461–470 (1976)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Jurdziński, T., Loryś, K.: Leftist Grammars and the Chomsky Hierarchy. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 293–304. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Lipton, R., Snyder, L.: A linear time algorithm for deciding subject security. Journal of the ACM 24(3), 455–464 (1977)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Motwani, R., Panigrahy, R., Saraswat, V.A., Venkatasubramanian, S.: On the decidability of accessibility problems (extended abstract). STOC, 306–315 (2000)Google Scholar
  10. 10.
    Saraswat, V.: The Matrix Design. Technical report, AT&T Laboratory (April 1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tomasz Jurdziński
    • 1
  1. 1.Institute of Computer ScienceWrocław UniversityWrocławPoland

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