Full characterisation of attractors of two intersected asynchronous Boolean automata cycles

Abstract

The understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems. In this paper, we make a step further in this understanding by focusing on their cycles, whose necessity in networks is known as the brick of their complexity. We present new results that provide a characterisation of the transient and asymptotic dynamics, i.e. of the computational abilities, of asynchronous Boolean automata networks composed of two cycles that intersect at one automaton, the so-called double-cycles. To do so, we introduce an efficient formalism inspired by algorithms to define long sequences of updates, that allows a better description of their dynamics than previous works in this area.