A general architecture of oritatami systems for simulating arbitrary finite automata

In this paper, we propose an architecture of oritatami systems, a mathematical model of RNA cotranscriptional folding, with which one can simulate an arbitrary nondeterministic finite automaton (NFA) in a unified manner. The oritatami system is known to be Turing-universal but the simulation available so far requires 542 bead types and O(t4log2⁡t) steps in order to simulate t steps of a Turing machine. The architecture we propose employs only 337 bead types and requires just O(t|Q|4|Σ|2) steps to simulate an NFA with a state set Q working on a word of length t over an alphabet Σ.