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Decision problem on interactions.

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Title: Decision problem on interactions.
Authors: Wachi, Hidetada1 (AUTHOR) wachi213@keio.jp
Source: International Journal of Algebra & Computation. May2026, Vol. 36 Issue 3, p285-298. 14p.
Subjects: Decidability (Mathematical logic), Conserved quantity
Abstract: An interaction is a certain symmetric graph that describes the possible transition of states of adjacent sites of large-scale interacting systems. In the series of studies [K. Bannai, Y. Kametani and M. Sasada, Topological structures of large-scale interacting systems via uniform functions and forms, Forum Math. Sigma 12 (2024) e107, doi: https://doi.org/10.1017/fms.2024.61 ], [K. Bannai and M. Sasada, Varadhan's decomposition of shift-invariant closed l 2 -forms for large-scale interacting systems on the euclidean lattice, preprint (2021), arXiv:2111.08934], they defined the notion of the irreducibly quantified interactions which is suitable for considering the hydrodynamic limits via the conserved quantities. In this paper, we prove that the property that an interaction is irreducibly quantified is decidable. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: An interaction is a certain symmetric graph that describes the possible transition of states of adjacent sites of large-scale interacting systems. In the series of studies [K. Bannai, Y. Kametani and M. Sasada, Topological structures of large-scale interacting systems via uniform functions and forms, Forum Math. Sigma 12 (2024) e107, doi: https://doi.org/10.1017/fms.2024.61 ], [K. Bannai and M. Sasada, Varadhan's decomposition of shift-invariant closed l 2 -forms for large-scale interacting systems on the euclidean lattice, preprint (2021), arXiv:2111.08934], they defined the notion of the irreducibly quantified interactions which is suitable for considering the hydrodynamic limits via the conserved quantities. In this paper, we prove that the property that an interaction is irreducibly quantified is decidable. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218196726500098
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 285
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      – SubjectFull: Decidability (Mathematical logic)
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              Text: May2026
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              Y: 2026
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