Ininvertible cellular automata: a review
Physica D
New types of diffusion in lattice gas cellular automata
Microscopic simulations of complex hydrodynamic phenomena
Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
Time-reversal symmetry in dynamical systems: a survey
Proceedings of the workshop on Time-reversal symmetry in dynamical systems
Periodicity and Immortality in Reversible Computing
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Journal of Computer and System Sciences
Bulking II: Classifications of cellular automata
Theoretical Computer Science
RC'13 Proceedings of the 5th international conference on Reversible Computation
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The notion of reversibility has been intensively studied in the field of cellular automata (CA), for several reasons. However, a related notion found in physical theories has been so far neglected, not only in CA, but generally in discrete dynamical systems. This is the notion of time-symmetry, which refers to the inability of distinguishing between backward and forward time directions. Here we formalize it in the context of CA, and study some of its basic properties. We also show how some well-known CA fit into the class of time-symmetric CA, and provide a number of results on the relation between this and other classes of CA. The existence of an intrinsically universal time-symmetric CA within the class of reversible CA is proved. Finally, we show the undecidability of time-symmetry for CA of dimension 2 or higher, even within the class of reversible CA. The case of dimension 1 is one of several open questions discussed in the conclusions.