  One of the characteristic features of genetic networks is their inherent
robustness, that is, their ability to retain functionality in spite of the
introduction of random errors. In this paper, we seek to better understand how
robustness is achieved and what functionalities can be maintained robustly. Our
goal is to formalize some of the language used in biological discussions in a
reasonable mathematical framework, where questions can be answered in a
rigorous fashion. These results provide basic conceptual understanding of
robust regulatory networks that should be valuable independent of the details
of the formalism.
  We model the gene regulatory network as a boolean network, a general and
well-established model introduced by Stuart Kauffman. A boolean network is said
to be in a viable configuration if the node states of the network at its
fixpoint satisfy some given constraint. We specify how mutations affect the
behavior of the boolean network. A network is then said to be robust if most
random mutations to the network reach a viable configuration. The main question
investigated in our study is: given a constraint on the fixpoint configuration,
does there exist a network that is robust with respect to it and, if so, what
is its structure? We demonstrate both explicit constructions of robust networks
as well as negative results disproving their existence.
