The Computational Power of Benenson Automata

TL;DR

This paper analyzes Benenson automata, a molecular computing scheme using DNA cutting, demonstrating their ability to compute arbitrary Boolean functions and efficiently simulate log-depth circuits, highlighting their potential in autonomous molecular decision-making.

Contribution

The paper introduces a formal model of Benenson automata, proving their computational universality and efficiency in simulating complex Boolean functions.

Findings

Benenson automata can simulate arbitrary Boolean circuits.

They are capable of computing exactly those functions with log-depth circuit complexity.

The study formalizes a new variant of limited width branching programs for molecular computation.

Abstract

The development of autonomous molecular computers capable of making independent decisions in vivo regarding local drug administration may revolutionize medical science. Recently Benenson at el (2004) have envisioned one form such a ``smart drug'' may take by implementing an in vitro scheme, in which a long DNA state molecule is cut repeatedly by a restriction enzyme in a manner dependent upon the presence of particular short DNA ``rule molecules.'' To analyze the potential of their scheme in terms of the kinds of computations it can perform, we study an abstraction assuming that a certain class of restriction enzymes is available and reactions occur without error. We also discuss how our molecular algorithms could perform with known restriction enzymes. By exhibiting a way to simulate arbitrary circuits, we show that these ``Benenson automata'' are capable of computing arbitrary Boolean functions. Further, we show that they are able to compute efficiently exactly those functions computable by log-depth circuits. Computationally, we formalize a new variant of limited width branching programs with a molecular implementation.