A Tight Linear Bound on the Neighborhood of Inverse Cellular Automata

  • Eugen Czeizler
  • Jarkko Kari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Eugen Czeizler
    • 1
    • 2
  • Jarkko Kari
    • 1
    • 3
  1. 1.Department of MathematicsUniversity of TurkuFinland
  2. 2.Turku Centre for Computer ScienceTurkuFinland
  3. 3.Department of Computer ScienceUniversity of IowaIowa CityUSA

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