Before revision:  Within this framework, we show that decidability imposes absolute limits to the  growth of complexity on computable dynamical systems up to a double logarithmic term . Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems.
After revision:  Within this framework, we show that decidability imposes absolute limits to the stable growth of complexity on computable dynamical systems up to a double logarithmic term . Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems.