Toward semantical model of reaction‐diffusion computing

The purpose of this paper is to fill a gap between experimental and abstract‐theoretic models of reaction‐diffusion computing. Chemical reaction‐diffusion computers are amongst leading experimental prototypes in the field of unconventional and nature‐inspired computing. In the reaction‐diffusion computers, the data are represented by concentration profiles of reagents, information is transferred by propagating diffusive and phase waves, computation is implemented in interaction of the traveling patterns, and results of the computation are recorded as a final concentration profile.

The paper analyzes a possibility of co‐algebraic representation of the computation in reaction‐diffusion systems using reaction‐diffusion cellular‐automata models.

Using notions of space‐time trajectories of local domains of a reaction‐diffusion medium the logic of trajectories is built, where well‐formed formulas and their truth‐values are defined by co‐induction. These formulas are non‐well‐founded set‐theoretic objects. It is demonstrated that the logic of trajectories is a co‐algebra.

The paper uses the logic defined to establish a semantical model of the computation in reaction‐diffusion media.

The work presents the first ever attempt toward mathematical formalization of reaction‐diffusion processes and is built building up semantics of reaction‐diffusion computing. It is envisaged that the formalism produced will be used in developing programming techniques of reaction‐diffusion chemical media.