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For rational numbers with Suppes-Ono division, equational validity is one-one equivalent with Diophantine unsolvability
Theoretical Computer Science, Volume: 1034, Start page: 115124
Swansea University Author:
John Tucker
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DOI (Published version): 10.1016/j.tcs.2025.115124
Abstract
Adding division to rings and fields leads to the question of how to deal with division by 0. From a plurality of options, we discuss in detail what we call Suppes-Ono division in which division by 0 produces 0. We explain the backstory of this semantic option and its associated notion of equality, a...
| Published in: | Theoretical Computer Science |
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| ISSN: | 0304-3975 1879-2294 |
| Published: |
Elsevier BV
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa68920 |
| Abstract: |
Adding division to rings and fields leads to the question of how to deal with division by 0. From a plurality of options, we discuss in detail what we call Suppes-Ono division in which division by 0 produces 0. We explain the backstory of this semantic option and its associated notion of equality, and prove a result regarding the logical complexity of deciding equations over the rational numbers equipped with Suppes-Ono division. We prove that deciding the validity of the equations is computationally equivalent to the Diophantine Problem for the rational numbers, which is a longstanding open problem. |
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| Keywords: |
Division by zero; Fracterm; Fracterm flattening; Diophantine equation; Decidability; 1-1 degrees |
| College: |
Faculty of Science and Engineering |
| Funders: |
Swansea University |
| Start Page: |
115124 |