Lapin, Yair (2021) Arithmetic logical Irreversibility and the Turing's Halt Problem. [Preprint]
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Abstract
A new approach to the halting problem of the Turing machine using different interpretations of the Shannon measure of the information on the computational process represented as a distribution of events (deleting, logical or arithmetic operations) and defining a new concept of arithmetic logical irreversibility and memory erasure that generate uncertainty and computational improbability due to loss of information during these events. Different computational steps (input) may give the same result (next step, output) introducing thus information entropy in the computing process and uncertainty about the original step (cause). This means that the same output may be produced by different inputs. Global indeterminism of computation as distribution but determinism of the computation as current process because the outputs are the same but the information not. The program or Turing machine as macro description of the computational states as micro description that they may be several and different but give the same result when they work .
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| Item Type: | Preprint | ||||||
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| Keywords: | Turing Halt problem, Gödel Theorem , Information Theory , Algorithmic information theory, Decision problem | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Computer Science Specific Sciences > Mathematics |
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| Depositing User: | mr Yair Lapin | ||||||
| Date Deposited: | 12 Apr 2022 16:19 | ||||||
| Last Modified: | 12 Apr 2022 16:19 | ||||||
| Item ID: | 20447 | ||||||
| Official URL: | https://www.academia.edu/49009877/Arithmetic_logic... | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Computer Science Specific Sciences > Mathematics |
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| Date: | 1 May 2021 | ||||||
| URI: | http://philsci-archive.pitt.edu/id/eprint/20447 |
Available Versions of this Item
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Arithmetic logical Irreversibility and the Turing's Halt Problem. (deposited 06 Mar 2022 20:27)
- Arithmetic logical Irreversibility and the Turing's Halt Problem. (deposited 12 Apr 2022 16:19) [Currently Displayed]
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