Physically-Relativized Church-Turing Hypotheses
arXiv:0805.1292 · doi:10.1016/j.amc.2009.04.062
Abstract
We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies, and causes for misunderstanding, concerning the state of the Church-Turing Hypothesis (CTH), suggests to study the CTH relative to an arbitrary but specific physical theory--rather than vaguely referring to ``nature'' in general. To this end we combine (and compare) physical structuralism with (models of computation in) complexity theory. The benefit of this formal framework is illustrated by reporting on some previous, and giving one new, example result(s) of computability and complexity in computational physics.
interdisciplinary paper: philosophy of physics, computational physics, computational complexity and computability
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