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The Complexity of Craig Interpolants

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Gems of Theoretical Computer Science
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Abstract

The Craig Interpolation Theorem (1957) was placed in the context of the P ≟ NP and NP ≟ coNP questions in a paper by Mundici (1984).

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References

  • M. Garey, D. Johnson: Computers and Intractability - A Guide to the Theory of NP-Completeness, Freeman, 1979.

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  • W. Craig: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory, Journal of Symbolic Logic 44 (1957) 36–50.

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  • E. Dahlhaus, A. Israeli, J.A. Makowsky: On the existence of polynomial time algorithms for interpolation problems in propositional logic, Notre Dame Journal on Formal Logic 29 (1988), 497–509.

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  • 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.

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  • D. Mundici: Tautologies with a unique Craig interpolant, uniform vs. nonuniform complexity, Annals of Pure and Applied Logic 27 (1984), 265–273.

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  • D. Mundici: NP and Craig’s interpolation theorem, in G. Lolli, G. Longo, A. Marja, ed., Logic Colloquium 82 North-Holland, 1984.

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  • U. Schoning, J. Toran: unpublished manuscript.

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© 1998 Springer-Verlag Berlin Heidelberg

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Schöning, U., Pruim, R. (1998). The Complexity of Craig Interpolants. In: Gems of Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60322-8_14

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  • DOI: https://doi.org/10.1007/978-3-642-60322-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64352-1

  • Online ISBN: 978-3-642-60322-8

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