Skip to main content
×
Home
    • Aa
    • Aa

THREE FORMS OF PHYSICAL MEASUREMENT AND THEIR COMPUTABILITY

  • EDWIN BEGGS (a1), JOSÉ FÉLIX COSTA (a2) and JOHN V TUCKER (a3)
Abstract
Abstract

We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct forms of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis.

Copyright
Corresponding author
*DEPARTMENT OF MATHEMATICS, COLLEGE OF SCIENCE SWANSEA UNIVERSITY, SINGLETON PARK, SWANSEA, SA2 8PP WALES, U.K. E-mail: e.j.beggs@swansea.ac.uk
INSTITUTO SUPERIOR TÉCNICO UNIVERSIDADE DE LISBOA PORTUGAL and CENTRO DE MATEMÁTICA E APLICAÇÕES FUNDAMENTAIS UNIVERSIDADE DE LISBOA PORTUGAL3 E-mail: fgc@math.tecnico.ulisboa.pt
DEPARTMENT OF COMPUTER SCIENCE, COLLEGE OF SCIENCE SWANSEA UNIVERSITY, SINGLETON PARK, SWANSEA, SA2 8PP WALES, U.K. E-mail: j.v.tucker@swansea.ac.uk
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. L. Balcázar , J. Días , & J Gabarró . (1995). Structural complexity I (second edition). Berlin: Springer-Verlag.

J. L. Balcázar , J. Días , & J Gabarró . (1990). Structural complexity II. Berlin: Springer-Verlag.

J. L. Balcázar , & M Hermo . (1998). The structure of logarithmic advice complexity classes. Theoretical Computer Science, 207(1), 217244.

E. Beggs , J. F. Costa , B. Loff , & J. V Tucker . (2008a). Computational complexity with experiments as oracles. Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences), 464(2098), 27772801.

E. Beggs , J. F. Costa , B. Loff , & J. V Tucker . (2008b). On the complexity of measurement in classical physics. In M. Agrawal , D. Du , Z. Duan , & A. Li , editors. Theory and applications of models of computation (TAMC 2008), Lecture Notes in Computer Science, Vol. 4978 , Berlin: Springer, pp. 2030.

E. Beggs , J. F. Costa , B. Loff , & J. V Tucker . (2009). Computational complexity with experiments as oracles II. Upper bounds. Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences), 465(2105), 14531465.

E. Beggs , J. F. Costa , D. Poças , & J. V Tucker . (2013a). On the power of threshold measurements as oracles. In G. Mauri , A. Dennunzio , L. Manzoni , & A. E. Porreca , editors. Unconventional computation and natural computation (UCNC 2013), Lecture Notes in Computer Science, Vol. 7956 , Berlin: Springer, pp. 618.

E. Beggs , J. F. Costa , D. Poças , & J. V Tucker . (2013b). Oracles that measure thresholds: The Turing machine and the broken balance. Journal of Logic and Computation, 23(6), 11551181.

E. Beggs , J. F. Costa , & J. V Tucker . (2012a). Axiomatising physical experiments as oracles to algorithms. Philosophical Transactions of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences), 370(12), 33593384.

E. Beggs & J. V Tucker . (2007). Experimental computation of real numbers by Newtonian machines. Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences), 463(2082), 15411561.

O. Bournez & M Cosnard . (1996). On the computational power of dynamical systems and hybrid systems. Theoretical Computer Science, 168(2), 417459.

R. Geroch & J. B Hartle . (1986). Computability and physical theories. Foundations of Physics, 16(6), 533550.

H. T Siegelmann . (1999). Neural networks and analog computation: Beyond the Turing limit, Switzerland: Birkhäuser.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 135 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.