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Abstract
Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.
Highlights
An abstract Turing Machine, in contrast to the 1-stack PDA, has access to a less limited memory, its tape, with unrestricted access because the head can move forward and backwards over the tape, and can read and write symbols on the tape
A common Turing Machine implementation[10,11] for recognizing the Dyck language is as follows: once the sequence is on the tape, the head is located at the first symbol and moves to the “right” looking for a closed parenthesis, marking it with a distinct symbol, e.g. X, and reversing the head direction until it finds the closest matching open parenthesis, overwriting it with an X and reversing again the head direction
If an open parenthesis is encountered before reaching the beginning of the expression, the automaton rejects the string
Summary
An abstract Turing Machine, in contrast to the 1-stack PDA, has access to a less limited memory, its tape, with unrestricted access because the head can move forward and backwards over the tape, and can read and write symbols on the tape. A common Turing Machine implementation[10,11] for recognizing the Dyck language is as follows: once the sequence is on the tape, the head is located at the first symbol and moves to the “right” looking for a closed parenthesis, marking it with a distinct symbol, e.g. X, and reversing the head direction (to the “left”) until it finds the closest matching open parenthesis, overwriting it with an X and reversing again the head direction.
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