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Alternation Trading Proofs and Their Limitations

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Mathematical Foundations of Computer Science 2013 (MFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8087))

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Abstract

Alternation trading proofs are motivated by the goal of separating NP from complexity classes such as Logspace or NL; they have been used to give super-linear runtime bounds for deterministic and co-nondeterministic sublinear space algorithms which solve the Satisfiability problem. For algorithms which use n o(1) space, alternation trading proofs can show that deterministic algorithms for Satisfiability require time greater than n cn for c < 2cos(π/7) (as shown by Williams [21,19]), and that co-nondeterministic algorithms require time greater than n cn for \(c<\sqrt[3]{4}\) (as shown by Diehl, van Melkebeek and Williams [5]). It is open whether these values of c are optimal, but Buss and Williams [2] have shown that for deterministic algorithms, c < 2cos(π/7) is the best that can obtained using present-day known techniques of alternation trading.

This talk will survey alternation trading proofs, and discuss the optimality of the unlikely value of 2cos(π/7).

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92130-0112, USA

    Sam Buss

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  1. Sam Buss
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Editors and Affiliations

  1. Institute for Science and Technology, 3400, Klosterneuburg, Austria

    Krishnendu Chatterjee

  2. Charles University, 11800, Prague, Czech Republic

    Jirí Sgall

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Buss, S. (2013). Alternation Trading Proofs and Their Limitations. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-40313-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40312-5

  • Online ISBN: 978-3-642-40313-2

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