Native Chemical Automata and the Thermodynamic Interpretation of Their Experimental Accept/Reject Responses

The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language classes. The function of the automata consists on recognizing words in a language generated by some grammar and expressed with letters from an alphabet. Such automata are, in principle, abstract entities and with suitable combinations of them we can represent any computation, no matter how complex. Their physical implementations are possible in any information carrying and recognition contexts and media, such as electrons in semiconductors, certain biomolecules in biology or even non-biological molecules. Here we describe and build non-biochemistry (inorganic chemistry) examples of a FA, PDA and TM computations carried out by specific laboratory realizations of the automata. For each of the three realizations we find a thermodynamic metric, based on enthalpy for the FA and PDA, and on the Gibbs free energy for the TM, to both assess the results of computation and as a first step towards quantifying the energetic cost of such computations.