On the cost of simulating a parallel Boolean automata network by a block-sequential one
Florian Bridoux, P. Guillon, Kévin Perrot, Sylvain Sené, Guillaume Theyssier · HAL (Le Centre pour la Communication Scientifique Directe) · 2017
In this article we study the minimum number $κ$ of additional automata that a Boolean automata network (BAN) associated with a given block-sequential update schedule needs in order to simulate a given BAN with a parallel update schedule. We introduce a graph that we call $\mathsf{NECC}$ graph built from the BAN and the update schedule. We show the relation between $κ$ and the chromatic number of the $\mathsf{NECC}$ graph. Thanks to this $\mathsf{NECC}$ graph, we bound $κ$ in the worst case between $n/2$ and $2n/3+2$ ($n$ being the size of the BAN simulated) and we conjecture that this number equals $n/2$. We support this conjecture with two results: the clique number of a $\mathsf{NECC}$ graph is always less than or equal to $n/2$ and, for the subclass of bijective BANs, $κ$ is always less than or equal to $n/2+1$.