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Logic Journal of IGPL Advance Access originally published online on August 29, 2006
Logic Journal of IGPL 2006 14(5):649-658; doi:10.1093/jigpal/jzl004
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Undecidability over Continuous Time

Jerzy Mycka

Institute of Mathematics, University of Maria Curie-Sklodowska, Lublin, Poland. E-mail: Jerzy.Mycka{at}umcs.lublin.pl

José Félix Costa

Department of Mathematics, I.S.T., Universidade Técnica de Lisboa, Lisboa, Portugal. E-mail: fgc{at}math.ist.utl.pt


  Abstract

Since 1996, some models of recursive functions over the real numbers have been analyzed by several researchers. It could be expected that they exhibit computational power much greater than that of Turing machines (as other well known models of computation over the real numbers already considered in the past fifteen years, like neural net models with real weights). The fact is that they do not have such power. Although they decide the classical halting problem of Turing machines, they otherwise have almost the same limitations of Turing machines.

Key Words: decidability • analog computation • real recursive functions


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