Spinal cellular automata

A special class of two-dimensional cellular automata (spinal automata) is defined. It is shown that the question whether a spinal automaton is injective is decidable, and the question whether a spinal automaton is reversible is decidable. In general those questions for two-dimensional cellular automata are undecidable. As language recognizers, the authors show that spinal automata are much more powerful than one-dimensional cellular automata.