2017/02/10 by Florian Bridoux, P. Guillon, Bridoux, Florian +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #Gene Regulatory Network Analysis
paper · doi:10.48550/arxiv.1702.03101
openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 NECC graph built from the BAN and the update schedule. We show the relation between κ and the chromatic number of the NECC graph. Thanks to this 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 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.