Lifespan in a strongly primitive Boolean linear dynamical system
Yaokun Wu, Yinfeng Zhu · 2015
Let F be a set of k by k nonnegative matrices such that every “long ” product of elements of F is positive. Cohen and Sellers (1982) proved that, then, every such product of length 2k−2 over F must be positive. They suggested to investigate the minimum size of such F for which there exists a non-positive product of length 2k−3 over F and they constructed one example of size 2k − 2. We construct one of size k and further discuss relevant basic problems in the framework of Boolean linear dynamical systems. We also formulate several primitivity properties for general discrete dynamical systems.