The Church-Turing Thesis: Breaking the Myth

  • Dina Goldin
  • Peter Wegner
Conference paper

DOI: 10.1007/11494645_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)
Cite this paper as:
Goldin D., Wegner P. (2005) The Church-Turing Thesis: Breaking the Myth. In: Cooper S.B., Löwe B., Torenvliet L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg

Abstract

According to the interactive view of computation, communication happens during the computation, not before or after it. This approach, distinct from concurrency theory and the theory of computation, represents a paradigm shift that changes our understanding of what is computation and how it is modeled. Interaction machines extend Turing machines with interaction to capture the behavior of concurrent systems, promising to bridge these two fields. This promise is hindered by the widespread belief, incorrectly known as the Church-Turing thesis, that no model of computation more expressive than Turing machines can exist. Yet Turing’s original thesis only refers to the computation of functions and explicitly excludes other computational paradigms such as interaction. In this paper, we identify and analyze the historical reasons for this widespread belief. Only by accepting that it is false can we begin to properly investigate formal models of interaction machines. We conclude the paper by presenting one such model, Persistent Turing Machines (PTMs). PTMs capture sequential interaction, which is a limited form of concurrency; they allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of Turing machines and of the Church-Turing thesis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dina Goldin
    • 1
  • Peter Wegner
    • 2
  1. 1.Computer Science & Engineering DepartmentUniversity of ConnecticutStorrsUSA
  2. 2.Computer Science DepartmentBrown UniversityProvidenceUSA

Personalised recommendations