Physical computation: How general are gandy's principles for mechanisms?

B. Jack Copeland, Oron Shagrir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


What are the limits of physical computation? In his 'Church's Thesis and Principles for Mechanisms', Turing's student Robin Gandy proved that any machine satisfying four idealised physical 'principles' is equivalent to some Turing machine. Gandy's four principles in effect define a class of computing machines ('Gandy machines'). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable.

Original languageAmerican English
Pages (from-to)217-231
Number of pages15
JournalMinds and Machines
Issue number2
StatePublished - Jul 2007

Bibliographical note

Funding Information:
Shagrir’s research was supported by the Israel Science Foundation, grant 857/03-07.


  • Accelerating turing machine
  • Asynchronous computation
  • Church's thesis
  • Davies
  • Determinism
  • Gandy
  • Hogarth
  • Hypercomputation
  • Physical computation
  • Pitowsky
  • Supertask
  • Thesis M


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