Decision problem on interactions

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 Bannai-Kametani-Sasada arXiv:2009.04699, Bannai-Sasada 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.

Figures (2)

• Figure 1: Interactions for $S = \{0,1,2,3,4\}$ which is exchangeable and separable but not irreducibly quantified.
• Figure 2: Irreducibly quantified interactions for $S = \{0,1,2,3,4\}$.

Theorems & Definitions (36)

• Definition 1.1: BS:Unif*Definition 1.2
• Definition 1.2: \ref{['def:irreq']}
• Theorem 1.3: \ref{['thm:decidable']}
• Theorem 1.4: NO89*Theorem 5.8
• Theorem 1.5: \ref{['thm:ccpcs-is-irred-q']}
• Definition 2.1
• Proposition 2.2
• proof
• Definition 2.3
• Remark 2.4