Ininvertible cellular automata: a review
Physica D
Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
The set of reversible 90/150 cellular automata is regular
Discrete Applied Mathematics
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
A new kind of science
Shift Register Sequences
The complexity of reversible cellular automata
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Graph Theory With Applications
Graph Theory With Applications
Finite automata and their decision problems
IBM Journal of Research and Development
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
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It is shown that the set of hybrid one-dimensional reversible cellular automata (CA) with the periodic boundary condition is a regular set. This has several important consequences. For example, it allows checking whether a given CA is reversible and the random generation of a reversible CA from the uniform distribution, both using time polynomial in the size of the CA. Unfortunately, the constant term in the resulting random generation algorithm is much too large to be of practical use. We show that for the less general case of null boundary (NB) CA, this constant can be reduced drastically, hence facilitating a practical algorithm for uniform random generation. Our techniques are further applied asymptotically to count the number of reversible NBCA.