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Spectral Problems and Descriptive Complexity Theory

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Gems of Theoretical Computer Science
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Abstract

This chapter begins with a question from predicate logic, namely to determine the set of all (sizes of) finite models of a given formula. It turns out that there is an amazingly close relationship between this question and the world of P and NP.

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References

  • H. Enderton: A Mathematical Introduction to Logic, Academic Press, 1972.

    Google Scholar 

  • H.J. Keisler, J. Robbin: Mathematical Logic and Computability, McGraw-Hill, 1996.

    Google Scholar 

  • C.H. Papadimitriou: Computational Complexity, Addison-Wesley, 1994, page 78.

    Google Scholar 

  • E. Borger: Decision problems in predicate logic, in G. Lolli, Florence Logic Colloquium 82, North-Holland.

    Google Scholar 

  • C.A. Christen: Spektralproblem und Komplexitatstheorie, in E. Specker, V. Strassen: Komplexitat von Entscheidungsproblemen, Lecture Notes in Computer Science 43, Springer, 1974, 102-126.

    Google Scholar 

  • R. Fagin: Generalized first-order spectra and polynomial-time recognizable sets, in R. Karp, ed., Complexity of Computation, SIAM-AMS Proceedings, Volume 7, 1974, 43-73.

    Google Scholar 

  • R. Fagin: Finite-model theory - a personal perspective, Theoretical Computer Science 116 (1993), 3–31.

    Article  MathSciNet  MATH  Google Scholar 

  • E. Gradel: The expressive power of second-order Horn logic, Proceedings of the 8th Symposium on Theoretical Aspects of Computer Science, Lecture Notes of Computer Science 480, Springer, 1991, 466-477.

    Google Scholar 

  • E. Gradel: Capturing complexity classes by fragments of second order logic, Proceedings of the 6th Structure in Complexity Theory Conference, IEEE, 1991, 341-352.

    Google Scholar 

  • Y. Gurevich: Toward logic tailored for computational complexity, in M.M. Richter et al, Computation and Proof Theory, Lecture Notes in Mathematics 1104, Springer, 1984, 175-216.

    Google Scholar 

  • N. Immerman: Expressibility as a complexity measure: results and directions, Proceedings of the 2nd Structure in Complexity Theory Conference, IEEE, 1987, 194-202.

    Google Scholar 

  • N. Immerman: Descriptive and computational complexity, in J. Hartmanis, ed., Computational Complexity Theory, AMS Applied Mathematics Proceedings, Vol. 38, 1989, 75-91.

    Google Scholar 

  • N.D. Jones, A.L. Selman: Turing machines and the spectra of first-order formulas, The Journal of Symbolic Logic 39, No. 1 (1974), 139–150.

    Article  MathSciNet  MATH  Google Scholar 

  • C.H. Papadimitriou: Computational Complexity, Addison-Wesley, 1994.

    Google Scholar 

  • L.J. Stockmeyer: The polynomial-time hierarchy, Theoretical Computer-Science 3 (1977), 1–22.

    Article  MathSciNet  MATH  Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Schöning, U., Pruim, R. (1998). Spectral Problems and Descriptive Complexity Theory. In: Gems of Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60322-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-60322-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64352-1

  • Online ISBN: 978-3-642-60322-8

  • eBook Packages: Springer Book Archive

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