{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T05:34:05Z","timestamp":1774935245912,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>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\u00a012 (2024) e107, doi: https:\/\/doi.org\/10.1017\/fms.2024.61 ], [K. Bannai and M. Sasada, Varadhan\u2019s decomposition of shift-invariant closed [Formula: see text]-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.<\/jats:p>","DOI":"10.1142\/s0218196726500098","type":"journal-article","created":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T02:41:11Z","timestamp":1766198471000},"page":"285-298","source":"Crossref","is-referenced-by-count":1,"title":["Decision problem on interactions"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-2958-6866","authenticated-orcid":false,"given":"Hidetada","family":"Wachi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama 223-8522, Japan"}]}],"member":"219","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"S0218196726500098BIB001","doi-asserted-by":"publisher","DOI":"10.1017\/fms.2024.61"},{"key":"S0218196726500098BIB002","unstructured":"K. Bannai, J. Koriki, M. Sasada, H. Wachi and S. 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