Refining Mark Burgin’s Case against the Church–Turing Thesis

Refining Mark Burgin’s Case against the Church–Turing Thesis

The outputs of a Turing machine are not revealed for inputs on which the machine fails to halt. Why is an observer not allowed to see the generated output symbols as the machine operates? Building on the pioneering work of Mark Burgin, we introduce an extension of the Turing machine model with a vis...

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Bibliographic Details
Published in:Philosophies (Basel) Vol. 9; no. 4; p. 122
Main Author: Daylight, Edgar Graham
Format: Journal Article
Language:English
Published: Basel MDPI AG 01-08-2024
Subjects:
Batch processing
Church–Turing thesis
Computer science
inductive Turing machine
Mark Burgin
Mathematical problems
Power
RBM
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Summary:The outputs of a Turing machine are not revealed for inputs on which the machine fails to halt. Why is an observer not allowed to see the generated output symbols as the machine operates? Building on the pioneering work of Mark Burgin, we introduce an extension of the Turing machine model with a visible output tape. As a subtle refinement to Burgin’s theory, we stipulate that the outputted symbols cannot be overwritten: at step i, the content of the output tape is a prefix of the content at step j, where i<j. Our Refined Burgin Machines (RBMs) compute more functions than Turing machines, but fewer than Burgin’s simple inductive Turing machines. We argue that RBMs more closely align with both human and electronic computers than Turing machines do. Consequently, RBMs challenge the dominance of Turing machines in computer science and beyond.
ISSN:2409-9287
2409-9287
DOI:10.3390/philosophies9040122