A Maximum Principle for Single-Input Boolean Control Networks

Boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks. We consider a Mayer-type optimal control problem for a single-input Boolean network, and derive a necessary condition for a control to be optimal. This provides an analog of Pontryagin's maximum principle for single-input Boolean networks.

I. Introduction

A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Cellular automata, with two possible states per cell, are a particular case of Boolean networks. Here, the state of each variable at time is determined by the state of its spatial neighbors at time [21].