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The Role of Observers in Computations

How Much Computation Does it Take to Recognize a Computation?

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Abstract

John Searle raised the question whether all computation is observer-relative. Indeed, all of the common views of computation, be they semantical, functional or causal rely on mapping something onto the states of a physical or abstract process. In order to effectively execute such a mapping, this process would have to be observed in some way. Thus a probably syntactical analysis by an observer seems to be essential for judging whether a given process implements some computation or not. In order to be able to explore the nature of these observers in a more formal way, we look at the Computing by Observing paradigm, a theoretical model of computation that includes an observer. We argue that the observers used there, monadic transducers, are good candidates for formalizing the way in which the syntax of a process must be analysed in order to judge whether it is computational.

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Notes

  1. In a setting like the one of the example of Sect. 2 we could imagine that for an addition \(14+32\) the process has to do the additions \(1+3\) and \(4+2\) separately; the observation does not contain these but only the compact result \(14+32\).

References

  • Aaronson, S. (2013). Why philosophers should care about computational complexity. In B. J. Copeland & O. S. C. Posy (Eds.), Computability: Turing, gdel, church, and beyond (pp. 261–328). London: MIT Press.

    Google Scholar 

  • Adleman, L. (1994). Molecular computation of solutions to combinatorial problems. Science, 226, 1021–1024.

    Article  Google Scholar 

  • Alhazov, A., & Cavaliere, M. (2004). Computing by observing bio-systems: The case of sticker systems. In C. Ferretti, G. Mauri, & C. Zandron (Eds.), DNA (Vol. 3384, pp. 1–13)., Lecture Notes in Computer Science Berlin: Springer.

    Google Scholar 

  • Bickle, J. (2013). Multiple realizability. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (2013th ed.). Berlin: Springer.

    Google Scholar 

  • Book, R., & Otto, F. (1993). String-rewriting systems. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Cavaliere, M., Frisco, P., & Hoogeboom, H. J. (2006). Computing by only observing. In O. H. Ibarra & Z. Dang (Eds.), Developments in language theory (Vol. 4036, pp. 304–314)., Lecture Notes in Computer Science Berlin: Springer.

    Chapter  Google Scholar 

  • Cavaliere, M., & Leupold, P. (2003). Evolution and observation: A new way to look at membrane systems. In C. Martín-Vide, G. Mauri, G. Paun, G. Rozenberg, & A. Salomaa (Eds.), Workshop on membrane computing (Vol. 2933, pp. 70–87). Lecture Notes in Computer Science, Berlin: Springer.

    Chapter  Google Scholar 

  • Cavaliere, M., & Leupold, P. (2004). Evolution and observation—A non-standard way to generate formal languages. Theoretical Computer Science, 321, 233–248.

    Article  MathSciNet  MATH  Google Scholar 

  • Cavaliere, M., & Leupold, P. (2006). Observation of string-rewriting systems. Fundamenta Informaticae, 74(4), 447–462.

    MathSciNet  MATH  Google Scholar 

  • Chalmers, D. J. (1996). Does a rock implement every finite-state automaton? Synthese, 108, 309–333.

    Article  MathSciNet  MATH  Google Scholar 

  • Dassow, J., Mitrana, V., & Salomaa, A. (2002). Operations and language generating devices suggested by the genome evolution. Theoretical Computer Science, 270(1–2), 701–738.

    Article  MathSciNet  MATH  Google Scholar 

  • Fodor, J. A. (1981). The mind–body problem. Scientific American, 241, 114–123.

    Article  Google Scholar 

  • Fresco, N. (2010). Explaining computation without semantics: Keeping it simple. Minds and Machines, 20, 165–181. https://doi.org/10.1007/s11023-010-9199-6.

    Article  Google Scholar 

  • Krassovitskiy, A., & Leupold, P. (2012). Computing by observing insertion. In A. H. Dediu & C. Martín-Vide (Eds.), LATA (Vol. 7183, pp. 377–388)., Lecture Notes in Computer Science Berlin: Springer.

    Google Scholar 

  • Landweber, L. F., & Kari, L. (2002). Universal molecular computation in ciliates. In L. F. Landweber & E. Winfree (Eds.), Evolution as computation, natural computing series (pp. 257–274). Berlin: Springer.

    Chapter  Google Scholar 

  • Morse, M. (1938). A solution of the problem of infinite play in chess. Bulletin of the American Mathemetical Society, 44, 632.

    Google Scholar 

  • Păun, G., Rozenberg, G., & Salomaa, A. (1998). DNA computing—New computing paradigms. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Piccinini, G. (2008). Computation without representation. Philosophical Studies, 137(2), 205–241. https://doi.org/10.1007/s11098-005-5385-4.

    Article  MathSciNet  Google Scholar 

  • Putnam, H. (1988). Representation and reality. London: MIT Press.

    Google Scholar 

  • Searle, J. R. (1992). The rediscovery of the mind. London: MIT Press.

    Google Scholar 

  • Turing, A. (1937). On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathematical Society, 2(42), 230–265.

    Article  MathSciNet  MATH  Google Scholar 

  • von Braunmühl, B., & Verbeek, R. (1979). Finite-change automata. In K. Weihrauch (Ed.), Theoretical computer science 4th GI conference (Vol. 67, pp. 91–100)., Lecture Notes in Computer Science Berlin: Springer.

    Chapter  Google Scholar 

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Acknowledgements

The two anonymous referees have invested a great amount of time in the long refereeing process and in sharing their knowledge in a very constructive way with the author. Thus they have effectuated several important changes in the manuscript and have had an essential part in letting it evolve to its current state. The author feels greatly indebted to both of the referees for their memorable patience and their openness of mind.

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Correspondence to Peter Leupold.

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Leupold, P. The Role of Observers in Computations. Minds & Machines 28, 427–444 (2018). https://doi.org/10.1007/s11023-018-9471-8

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