Proof of Church's Thesis

Church's thesis, "consistency", "formalization", "proof theory" : dictionary entries

Church's Thesis Meets Quantum Mechanics

| \Church's thesis" is the notion that any \reasonable physical system" may be \simulated" by a Turing machine. The \strong" Church's thesis adds \...with at most polynomial slowdown." The \in-termediate" Church's thesis (my own invention) instead says \...with at most polynomial ampliication of memory-space requirements." (All the terms in quotes need to be deened.) In your favorite set of phy...

Church's thesis meets the N-body problem

“Church’s thesis” is at the foundation of computer science. We point out that with any particular set of physical laws, Church’s thesis need not merely be postulated, in fact it may be decidable. Trying to do so is valuable. In Newton’s laws of physics with point masses, we outline a proof that Church’s thesis is false; phsyics is unsimulable. But with certain more realistic laws of motion, inc...

The Narrational Case Against Church's Thesis

In a recent and widely aarmed paper in this journal, Elliot Mendelson 27] 1 challenges what he rightly calls the \standard conception" (230) of Church's Thesis (CT) | the conception being that CT is unprovable. Unfortunately, as I demonstrate herein, once Mendelson's target, and his attack upon it, are rigorously analyzed with help from uncomputability theory, his challenge evaporates, and the ...

Church's thesis and its epistemological status

The aim of this paper is to present the origin of Church’s thesis and the main arguments in favour of it as well as arguments against it. Further the general problem of the epistemological status of the thesis will be considered, in particular the problem whether it can be treated as a definition and whether it is provable or has a definite truth-value. 1. Origin and various formulations of Chu...

A Natural Axiomatization of Computability and Proof of Church's Thesis

Church’s Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turingcomputable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic...