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RETRACTED CHAPTER: Complete Disjoint CoNP-Pairs but No Complete Total Polynomial Search Problems Relative to an Oracle

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Fundamentals of Computation Theory (FCT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11651))

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Abstract

Consider the following conjectures:

  • \(\mathsf {TFNP}\): the set TFNP of all total polynomial search problems has no complete problems with respect to polynomial reductions.

  • \(\mathsf {DisjCoNP}\): there exists no many-one complete disjoint coNP-pair.

We construct an oracle relative to which \(\mathsf {TFNP}\) holds and \(\mathsf {DisjCoNP}\) does not hold. This partially answers a question by Pudlák [12], who lists several conjectures and asks for oracles that show corresponding relativized conjectures to be different. As there exists a relativizable proof for the implication \(\mathsf {DisjCoNP}\Rightarrow \mathsf {TFNP}\) [12], relative to our oracle the conjecture \(\mathsf {TFNP}\) is strictly stronger than \(\mathsf {DisjCoNP}\).

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Change history

  • 07 February 2020

    The author has retracted this chapter [1] because of a gap in the proof of the main theorem caused by an incorrect application of Claim 4. The author agrees to this retraction.

References

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Titus Dose

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  1. Titus Dose
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Correspondence to Titus Dose .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Leszek Antoni Gąsieniec

  2. Hong Kong Polytechnic University, Hong Kong, China

    Jesper Jansson

  3. Lund University, Lund, Sweden

    Christos Levcopoulos

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Dose, T. (2019). RETRACTED CHAPTER: Complete Disjoint CoNP-Pairs but No Complete Total Polynomial Search Problems Relative to an Oracle. In: Gąsieniec, L., Jansson, J., Levcopoulos, C. (eds) Fundamentals of Computation Theory. FCT 2019. Lecture Notes in Computer Science(), vol 11651. Springer, Cham. https://doi.org/10.1007/978-3-030-25027-0_11

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  • DOI: https://doi.org/10.1007/978-3-030-25027-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25026-3

  • Online ISBN: 978-3-030-25027-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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