How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata

This manuscript contains the experimental realization of one instance of each automata in the theory of computation using chemistry and not using biochemistry. All automata are implemented in a 1-pot reactor. The Finite Automaton (FA) is represented by a precipitation reaction, the 1-stack Push Down Automaton (PDA) by a pH reaction network and the Turing machine (TM) by the Belousov-Zhabotinsky chemical reaction. The computation (consisting on recognizing if chemically transcribed abstract sequences belong to appropriate languages in the Chomsky hierarchy) is carried out by a chemical reaction recognizing the molecules and their order. Once the sequence is introduced in the reactor (very much as mRNA is introduced in the ribosome) the reaction does all the recognition without any need for external not strictly chemical help from reaction/diffusion set-ups or chemical gates. The result of the computation has a straightforward thermodynamic/information theory interpretation. These results are of interest for soft-robotics, chemically self-assembled systems, chemical neural networks, artificial intelligence and of course chemical computing (i. e., computing done by chemistry at molecular scales which translates to larger scales by the power of Avogadro's number) as well as natural computing and analog/digital computing.