Undecidable properties on the dynamics of reversible one-dimensional cellular automata

Many properties of the dynamics of one-dimensional cellular automata are known to be undecidable. However, the undecidability proofs often rely on the undecid- ability of the nilpotency problem, and hence cannot be applied in the case the automaton is reversible. In this talk we review some recent approaches to prove dynamical properties of reversible 1D CA undecidable. Properties considered include equicontinuity (=periodic- ity), sensitivity, variants of mortality, one-sided expansivity and regularity. All these prop- erties are undecidable, according to recent proofs obtained in collaboration with N.Ollinger or V.Lukkarila.