A general architecture of oritatami systems for simulating arbitrary finite automata

Abstract

In this paper, we propose an architecture of oritatami systems 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 $O(t^4{\log }^{2}t)$ steps in order to simulate $t$ steps of a Turing machine. The architecture we propose employs only 329 bead types and requires just $O(t|Q{|}^4|\hat{I}\pounds {|}^2)$ steps to simulate an NFA over an input alphabet $\hat{I}\pounds$ with a state set $Q$ working on a word of length $t$.