Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Time/space trade-offs for reversible computation
SIAM Journal on Computing
Ininvertible cellular automata: a review
Physica D
Linear logic and permutation stacks—the Forth shall be first
ACM SIGARCH Computer Architecture News - Special issue: panel sessions of the 1991 workshop on multithreaded computers
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
On the circuit depth of structurally reversible cellular automata
Fundamenta Informaticae - Special issue dedicated to A. Salomaa
A new kind of science
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Cellular automata mechanics.
A pedestrian's introduction to spacetime crystallography
IBM Journal of Research and Development
How to turn a second-order cellular automaton into a lattice gas: a new inversion scheme
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Theory of cellular automata: a survey
Theoretical Computer Science
Irreversibility and heat generation in the computing process
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
On Pattern Density and Sliding Block Code Behavior for the Besicovitch and Weyl Pseudo-distances
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codes
Theoretical Computer Science
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Both cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the terms 'cellular automaton' and 'lattice gas' for a dynamic system itself as well as for its presentation. The two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability. Following a conjecture by Toffoli and Margolus, it had been proved by Kari that any invertible CA, at least up to two dimensions, can be rewritten as an isomorphic LG. But until now it was not known whether this is possible in general for noninvertible CA-which comprise ''almost all'' CA and represent the bulk of examples in theory and applications. Even circumstantial evidence-whether in favor or against-was lacking. Here, for noninvertible CA, (a) we prove that an LG presentation is out of the question for the vanishingly small class of surjective ones. We then turn our attention to all the rest-noninvertible and nonsurjective-which comprise all the typical ones, including Conway's 'Game of Life'. For these (b) we prove by explicit construction that all the one-dimensional ones are representable as LG, and (c) we present and motivate the conjecture that this result extends to any number of dimensions. The tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale.