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Journal of Computer Science and Technology

, Volume 15, Issue 5, pp 439–444 | Cite as

Some structural properties of SAT

  • Liu Tian Email author
Article
  • 25 Downloads

Abstract

The following four conjectures about structural properties of SAT are studied in this paper. (1) SAT ∈P SPARSE∩NP; (2) SAT ∈SRTD tt; (3) SAT ∈P tt bAPP ; (4)FP tt SAT . It is proved that some pairs of these conjectures implyP=NP, for example, if\(SAT \in P^{SPARSE \cap NP} \) and SAT ∈p tt bAPP , or if SAT ∈SRTD tt and SAT ∈P tt bAPP , thenP=NP. This improves previous results in literature.

Keywords

structural complexity SAT sparse set approximable set truthtable reduction non-adaptive search reducible to decision 

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References

  1. [1]
    Naik A N, Selman A L. A note onP-selective sets and on adaptive versus nonadaptive queries to NP. InProceeding of the 11th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press, 1996, pp.2–15.Google Scholar
  2. [2]
    Buhrman H, Fortnow L, Thierauf T. Six hypotheses in search of a theorem. InProceedings of the 12th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press, 1997, pp.2–12.Google Scholar
  3. [3]
    Ogiwara M, Watanabe O. On polynomial time bounded truth-table reducibility of NP sets to sparse sets.SIAM Journal on Computing, 1991, 20: 471–483.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Ogihara M. Polynomial-time membership comparable sets.SIAM Journal on Computing, 1995, 24: 1068–1081.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Karp R M, Ripton R J. Some connections between nonuniform and uniform complexity classes. InProceedings of the 12th Annual ACM Symposium on the Theory of Computing, ACM Press, 1980, pp.302–309.Google Scholar
  6. [6]
    Köbler J, Watanabe O. New collapse consequences of NP having small circuits.SIAM Journal on Computing, 1999, 28: 311–324.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Lutz J H, Mayordomo E. Measure, stochasticity, and the density of hard languages.SIAM Journal on Computing, 1994, 23: 762–779.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Wang Y. NP-hard sets are superterse unless NP is small. Technical Report TR97-021, Electronic Colloquium on Computational Cmplexity, URL: http://www.eccc.uni-trier.de/eccc/,1996.Google Scholar
  9. [9]
    Kadin J.N NP[log] and sparse Turing-complete sets for NP.Journal of Computer and System Sciences, 1989, 39: 282–298.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Arvind V, Toran J. Sparse sets, approximable sets, and parallel queries to NP. Technical Report TR98-027, Electronic Colloquium on Computational Cmplexity, URL: http://www.eccc.uni-trier.de/eccc/, 1998.Google Scholar
  11. [11]
    Watanabe O, Toda S. Structural analysis on the complexity of inverse functions.Mathematical Systems Theory, 1993, 26: 203–214.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Buhrman H, Thierauf T. The complexity of generating and checking proofs of membership. InProceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science #1046, Springer-Verlag, 1996, pp.75–86.Google Scholar
  13. [13]
    Buhrman H, Fortnow L. Resource-bounded Kolmogorov complexity revisited. InProceedings of the 24th Annual International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science #1200, Springer-Verlag, 1997, pp.105–116.Google Scholar
  14. [14]
    Amir A, Beigel R, Gasarch W I. Some connections between bounded-query classes and nonuniform complexity. InProceedings of the 5th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press, 1990, pp.232–243.Google Scholar
  15. [15]
    Beigel R. NP hard sets areP superterse unlessR=NP. Technical Report 88-04, Department of Computer Science, The Johns Hopkins University, 1988.Google Scholar
  16. [16]
    Toda S. On polynomial time truth-table reducibility of intractable sets toP-selective sets.Mathematical Systems Theory, 1991, 24: 69–82.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    Selman A. A taxonomy of complexity classes of functions.Journal of Computer and System Sciences, 1994, 48: 357–381.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Balcázar J L, Díaz J, Gabaró J. Structural Complexity Theory, I, II. Springer-Verlag, 1988, 1990.Google Scholar
  19. [19]
    Papadimitriou C H. Computational Complexity. Addison-Wesley, 1994.Google Scholar
  20. [20]
    Köbler J, Thierauf T. Complexity-restricted advice functions.SIAM Journal on Computing, 1994, 23: 261–275.zbMATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    Krentel M W. The complexity of optimization problems.Journal of Computer and System Sciences, 1988, 36: 490–509.zbMATHCrossRefMathSciNetGoogle Scholar
  22. [22]
    Selman A. Much ado about functions. InProceedings of the 11th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press, 1996, pp.2–14.Google Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2000

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyPeking UniversityBeijingP.R. China

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