Joint realizability of monotone Boolean functions

The study of monotone Boolean functions (MBFs) has a long history. We explore connection between MBFs and ordinary differential equation (ODE) models gene regulation, and, in particular, problem the realization an MBF as function describing state transition graph ODE. formulate joint realizability finite collections by establishing parameterized dynamics class ODEs collection MBFs. pose question what can be realized that belong to nested classes defined increased algebraic complexity their right-hand sides. As we progressively restrict form ODE, show combination theory explicit examples jointly realizable strictly decreases. Our results impact regulatory network dynamics, well classical area conclude with series potential extensions conjectures.