Defining Wall-Mode Snake: A Taxonomy of States and Constraints for AI Research

Wall-mode Snake introduces dynamically appearing obstacles that progressively constrain a grid as the snake grows, creating a planning problem with long-horizon survivability constraints. This paper proposes a reproducible reference formulation of wall-mode Snake and introduces a constraint-based taxonomy of board states intended to support interpretable analysis beyond aggregate score metrics. The taxonomy identifies recurring structural failure modes—including connectivity loss, bottlenecks, pocket formation, corridor forcing, parity stress, and head–tail inaccessibility—and provides canonical examples for each. Rather than proposing a new agent, the paper aims to clarify problem definition and enable more systematic comparison across algorithmic approaches. This work is intended for researchers in algorithmic game theory, AI planning, search, and grid-based decision processes.