Ininvertible cellular automata: a review
Physica D
Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
A new kind of science
Tessellations with local transformations
Journal of Computer and System Sciences
Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Journal of Computer and System Sciences
A tight linear bound on the synchronization delay of bijective automata
Theoretical Computer Science
Fast reversible language recognition using cellular automata
Information and Computation
Real-time reversible iterative arrays
Theoretical Computer Science
Linear algebra based bounds for one-dimensional cellular automata
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Real-time reversible iterative arrays
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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Reversible cellular automata (RCA) are models of massively parallel computation that preserve information. They consist of an array of identical finite state machines that change their states synchronously according to a local update rule. By selecting the update rule properly the system has been made information preserving, which means that any computation process can be traced back step-by-step using an inverse automaton. We investigate the maximum range in the array that a cell may need to see in order to determine its previous state. We provide a tight upper bound on this inverse neighborhood size in the one-dimensional case: we prove that in a RCA with n states the inverse neighborhood is not wider than n–1, when the neighborhood in the forward direction consists of two consecutive cells. Examples are known where range n–1 is needed, so the bound is tight. If the forward neighborhood consists of m consecutive cells then the same technique provides the upper bound nm−1–1 for the inverse direction.