Decision problem on interactions

TL;DR

This paper proves that determining whether an interaction, modeled as a symmetric graph describing state transitions in large systems, is irreducibly quantified is a decidable problem, advancing understanding of hydrodynamic limits.

Contribution

It establishes the decidability of the irreducibly quantified interaction property, a key concept for analyzing hydrodynamic limits in large-scale systems.

Findings

Proves the property of being irreducibly quantified is decidable.

Builds on previous definitions of irreducibly quantified interactions.

Supports analysis of hydrodynamic limits in interacting systems.

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.