Reaction systems with self distinction

We proceed in the investigation of models of environment in reaction systems, beyond the simple models establishing context-independent or arbitrary processes, to consider restrictions on both the sets of entities that an environment can contribute to a reaction system and the set of entities that a reaction system can produce. Such a distinction is reminiscent of that between self and non-self in living systems and is examined in this paper under different respects. We discuss applications of the model to living systems and security, as well as relations between families of reaction systems with self distinction, unveiling peculiarities of processes with self distinction with respect to the classical notion, for both context-independent processes and processes with arbitrary context. In particular, we introduce a notion of simulation, through which we show that the restriction to systems with self distinction does not entail any loss in the set of realisable behaviours, and that there exists a family of reaction systems with self distinction able to simulate context-independent behaviours of classical reaction systems through processes with arbitrary context. Moreover, using 2-step simulations, we show that every reaction system with self distinction can be reduced to a system (with self-distinction) using only reactions where no set of reactants and inhibitors mixes entities from both the self and the non-self sets.