TL;DR
This paper proves that if our computational model is a universal Turing machine with finite tape, then Church's thesis holds, completing Post's 1936 program to establish the thesis's validity.
Contribution
It provides a formal proof confirming Church's thesis based on the finite tape model of universal Turing machines, fulfilling Post's longstanding goal.
Findings
Church's thesis is proven true under the finite tape Turing machine model
The proof completes Post's 1936 program for Church's thesis
Supports the universality of Turing machines in computational theory
Abstract
We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Cellular Automata and Applications