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Invited Paper: How Do Humans Succeed in Tasks Like Proving Fermat’s Theorem or Predicting the Higgs Boson?

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Stabilization, Safety, and Security of Distributed Systems (SSS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14310))

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Abstract

I discuss issues of inverting feasibly computable functions, optimal discovery algorithms, and the constant overheads in their performance.

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Notes

  1. 1.

    This is a complete problem, i.e. all other inversion problems are reducible to it.

References

  1. Baker, T.P., Gill, J., Solovay, R.: Relativizations of the P = NP question. SIComp 4(4), 431–442 (1975)

    Article  MATH  Google Scholar 

  2. Cook, S.: The complexity of theorem proving procedures. In: STOC-1971, pp. 151–158 (1971)

    Google Scholar 

  3. Dekhtiar, M.: On the impossibility of eliminating exhaustive search in computing a function relative to its graph. Russ. Proc. USSR Acad. Sci. 14, 1146–1148 (1969)

    Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman (1979)

    Google Scholar 

  5. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum (1972)

    Google Scholar 

  6. Kolmogorov, A.N., Uspenskii, V.A.: On the definition of an algorithm. Uspekhi Mat. Nauk 13(4), 3–28 (1958). AMS Transl. 1963. 2nd ser. 29:217–245

    Google Scholar 

  7. Levin, L.A.: Универсальные Задачи Перебора (1973). (in Russian) [Universal search problems]. Probl. Inf. Transm. 9(3), 115–116. English Translation in [9]

    Google Scholar 

  8. Levin, L.A.: Universal heuristics: how do humans solve “unsolvable” problems? In: Dowe, D.L. (ed.) Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence. LNCS, vol. 7070, pp. 53–54. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-44958-1_3. Also in a CCR/SIGACT Workshop Report “Visions for Theoretical Computer Science”

  9. Trakhtenbrot, B.A.: A survey of Russian approaches to perebor (brute-force search) algorithms. Ann. Hist. Comput. 6(4), 384–400 (1984)

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Authors and Affiliations

  1. Boston University, Boston, MA, 02215, USA

    Leonid A. Levin

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  1. Leonid A. Levin
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Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be'er-Sheva, Israel

    Shlomi Dolev

  2. New Jersey Institute of Technology, Newark, NJ, USA

    Baruch Schieber

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Levin, L.A. (2023). Invited Paper: How Do Humans Succeed in Tasks Like Proving Fermat’s Theorem or Predicting the Higgs Boson?. In: Dolev, S., Schieber, B. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2023. Lecture Notes in Computer Science, vol 14310. Springer, Cham. https://doi.org/10.1007/978-3-031-44274-2_38

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  • DOI: https://doi.org/10.1007/978-3-031-44274-2_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-44273-5

  • Online ISBN: 978-3-031-44274-2

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