Solution searching that accompanies combinatorial explosion is one of the most important issues in the age of artificial intelligence. Natural intelligence, which exploits natural processes for intelligent functions, is expected to help resolve or alleviate the difficulties of conventional computing paradigms and technologies. In fact, we have shown that a single-celled organism such as an amoeba can solve constraint satisfaction problems and related optimization problems as well as demonstrate experimental systems based on non-organic systems such as optical energy transfer involving near-field interactions. However, the fundamental mechanisms and limitations behind solution searching based on natural processes have not yet been understood. Herein, we present a theoretical background of solution searching based on optical excitation transfer from a category-theoretic standpoint. One important indication inspired by the category theory is that the satisfaction of short exact sequences is critical for an adequate computational operation that determines the flow of time for the system and is termed as “short-exact-sequence-based time
.” In addition, the octahedral and braid structures known in triangulated categories provide a clear understanding of the underlying mechanisms, including a quantitative indication of the difficulties of obtaining solutions based on homology dimension. This study contributes to providing a fundamental background of natural intelligence.
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