Decision problem on interactions

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: 10.1017/fms.2024.61], [K. Bannai and M. Sasada, Varadhan’s 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.