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Algorithm Analysis Through Proof Complexity

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Sailing Routes in the World of Computation (CiE 2018)

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Abstract

Proof complexity can be a tool for studying the efficiency of algorithms. By proving a single lower bound on the length of certain proofs, we can get running time lower bounds for a wide category of algorithms. We survey the proof complexity literature that adopts this approach relative to two \(\mathsf {NP}\)-problems: k-clique and 3-coloring.

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Notes

  1. 1.

    The possibility of short proofs for all tautologies was already mentioned by Gödel in a letter to von Neumann [27].

  2. 2.

    A SAT solver is a software that decides satisfiability. While nowadays solvers go beyond resolution, their main component still builds resolution proofs.

  3. 3.

    The graph has n vertices and the edges are independent \(\{0,1\}\)-valued random variables with expected value p.

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, Università “La Sapienza” di Roma, Rome, Italy

    Massimo Lauria

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  1. Massimo Lauria
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  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Lauria, M. (2018). Algorithm Analysis Through Proof Complexity. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_26

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