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The Complexity of Pure Literal Elimination

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SAT 2005
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Abstract

The computational complexity of eliminating pure literals is calibrated for various classes of CNF formulas. The problem is shown to be P-complete in general, NL-complete for 2-CNF, and SL-complete for CNF formulas with at most two occurrences of each variable.

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References

  • Davis, M., Logemann, G. and Loveland, D. (1962) A machine program for theorem proving, Commun. ACM 5, pp. 394–397.

    Article  MathSciNet  Google Scholar 

  • Goldberg, E. and Novikov, Y. (2002) BerkMin: a fast and robust SAT-solver, in Design, Automation, and Test in Europe (DATE’ 02), pp. 142–149.

    Google Scholar 

  • Greenlaw, R., Hoover, H. J. and Ruzzo, W. L. (1995) Limits to Parallel Computation, Oxford University Press.

    Google Scholar 

  • Johannsen, J. (2004) Satisfiability problems complete for deterministic logarithmic space, in V. Diekert and M. Habib (eds.), 21st International Symposium on Theoretical Aspects of Computer Science (STACS 2004), pp. 317–325.

    Google Scholar 

  • Jones, N. D. (1975) Space bounded reducibility among combinatorial problems, J. Comput. Syst. Sci. 11, pp. 65–85.

    Google Scholar 

  • Jones, N. D., Lien, Y. E. and Laaser, W. T. (1976) New problems complete for nondeterministic log space, Math Syst. Theory. 10, pp. 1–17.

    Article  MathSciNet  Google Scholar 

  • Kullmann, O. (1999) New methods for 3-SAT decision and worst-case analysis, Theor. Comp. Sci. 223(1–2), pp. 1–72.

    Article  MathSciNet  Google Scholar 

  • Kullmann, O. (2002) Investigating the behaviour of a SAT solver on random formulas, Submitted.

    Google Scholar 

  • Le Berre, D., Simon, L. and Tacchella, A. (2003) Challenges in the QBF arena: the SAT’03 evaluation of QBF solvers, in Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT2003), pp. 468–485, Springer LNCS 2919.

    Google Scholar 

  • Letz, R. (2002) Lemma and model caching in decision procedures for quantified Boolean formulas, in U. Egly and C. G. Fermüller (eds.), TABLEAUX 2002, pp. 160–175.

    Google Scholar 

  • Letz, R. (2004) personal communication.

    Google Scholar 

  • Lewis, H. R. and Papadimitriou, C. H. (1982) Symmetric space-bounded computation, Theor. Comp. Sci. 19, pp. 161–187.

    Article  MathSciNet  Google Scholar 

  • Moskewicz, M. W., Madigan, C. F., Zhao, Y., Zhang, L. and Malik, S. (2001) Chaff: Engineering an efficient SAT solver, in Proceedings of the 38th Design Automation Conference (DAC’01).

    Google Scholar 

  • Nisan, N. and Ta-Shma, A. (1995) Symmetric logspace is closed under complement, Chic. J. Theor. Comput. Sci.

    Google Scholar 

  • Reingold, O. (2005) Undirected ST-connectivity in log-space, To appear in Proceedings of the 37th ACM Symposium on Theory of Computing.

    Google Scholar 

  • Schiermeyer, I. (1996) Pure literal lookahead: an O(1.497n) 3-satisfiability algorithm, in J. Franco, G. Gallo, H. Kleine Büning, E. Speckenmeyer and C. Spera (eds.), Workshop on the Satisfiability Problem.

    Google Scholar 

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© 2005 Springer

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Johannsen, J. (2005). The Complexity of Pure Literal Elimination. In: Giunchiglia, E., Walsh, T. (eds) SAT 2005. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5571-3_6

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  • DOI: https://doi.org/10.1007/978-1-4020-5571-3_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4552-3

  • Online ISBN: 978-1-4020-5571-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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