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TFNP: An Update

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Algorithms and Complexity (CIAC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

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Abstract

The class TFNP was introduced a quarter of a century ago to capture problems in NP that have a witness for all inputs. A decade ago, this line of research culminated in the proof that the Nash equilibrium problem is complete for the subclass PPAD. Here we review some interesting developments since.

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Notes

  1. 1.

    Notice immediately that there is a trivial way of combining any finite number of classes with complete problems via some kind of “direct product” construction to obtain one all-encompassing class and complete problem. The challenge is to do this in a way that does not explicitly refer to the parts.

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Acknowledgments

Many thanks to the “PPAD-like classes reading group” at the Simons Institute during the Fall 2015 program on Economics and Computation for many fascinating interactions. We also thank Arnold Beckmann, Pavel Pudlák, and Sam Buss for helpful discussions. Work supported by NSF grant CCF-1408635.

Author information

Authors and Affiliations

  1. University of Oxford, Oxford, UK

    Paul W. Goldberg

  2. University of California at Berkeley, Berkeley, USA

    Christos H. Papadimitriou

Authors
  1. Paul W. Goldberg
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  2. Christos H. Papadimitriou
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Correspondence to Christos H. Papadimitriou .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Goldberg, P.W., Papadimitriou, C.H. (2017). TFNP: An Update. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57585-8

  • Online ISBN: 978-3-319-57586-5

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