(untitled) (Journal of Informatics and Mathematical Sciences, 2011)
E. Remy, P. Ruet and D. Thieffry have proved a Boolean version of Thomas’ conjecture: if a map F from {0,1}^n to itself has several fixed points, then there exists a positive circuit in the corresponding interaction graph. In this paper, we prove that the presence of a positive circuit in a local interaction graph is also a necessary condition for the presence of several attractive cycles in the Boolean synchronous dynamics.