Resolve the reversibility problem for general one-dimensional cellular automata

Establish a complete resolution of the reversibility problem for general one-dimensional cellular automata on Z^1 by providing a characterization or decision procedure that determines, for any given local rule and finite state set, whether the induced global map is bijective.

Background

The paper surveys prior results: reversibility is undecidable in dimensions two and higher, specific subclasses such as number-conserving CA have been settled, and linear finite CA have partial characterizations. The authors present an efficient method that completely solves reversibility for one-dimensional finite cellular automata (FCA), including determining periodicity in reversibility as the number of cells grows.

Despite these advances for finite systems, the broader problem for general (non-finite) one-dimensional cellular automata remains unresolved according to the authors, indicating a gap between the finite and infinite-lattice settings.