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 n m-1 - 1 for the inverse direction. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Czeizler, E., & Kari, J. (2005). A tight linear bound on the neighborhood of inverse cellular automata. In Lecture Notes in Computer Science (Vol. 3580, pp. 410–420). Springer Verlag. https://doi.org/10.1007/11523468_34
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