Surjective cellular automata far from the Garden of Eden
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Summary
It is shown that several other results from the literature, already known to characterize surjective cellular automata in dimension d, hold precisely when the Garden-of-Eden theorem does, and the amount of such failure is measured.
- Type
- article
- Published
- 2013-10-18
- Cited by
- 10
- References
- 27
- Access
- Open access
- OpenAlex
- https://openalex.org/W34927876
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:15161379
Keywords
Mathematics, Surjective function, Cellular automaton, Garden of Eden, Automaton
References
- SOFIC GROUPS AND DYNAMICAL SYSTEMS
- Algorithmic Randomness and Complexity
- Introduction to the Modern Theory of Dynamical Systems
- Condition for Injectivity of Global Maps for Tessellation Automata
- Gardens of Eden and amenability on cellular automata
- Garden of Eden Configurations for Cellular Automata on Cayley Graphs of Groups
- Entropy and isomorphism theorems for actions of amenable groups
- A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
- The converse of Moore’s Garden-of-Eden theorem
- Randomness on full shift spaces
- Computable algebra, general theory and theory of computable fields.
- On the definition of normal numbers
- The Axiomatization of Randomness
- The Definition of Random Sequences
- Induction and restriction of cellular automata
- Combinatorial Group Theory
- Amenable groups and cellular automata
- Introduction to the modern theory of dynamical systems
- Cellular Automata and Groups
- Combinatorial Group Theory.
Cited by
- Post-surjectivity and balancedness of cellular automata over groups
- Freezing, Bounded-Change and Convergent Cellular Automata
- Besicovitch Pseudodistances with Respect to Non-Følner Sequences
- Cellular Automata and Discrete Complex Systems
- Cellular Automata and Discrete Complex Systems: 26th IFIP WG 1.5 International Workshop, AUTOMATA 2020, Stockholm, Sweden, August 10–12, 2020, Proceedings
- Cold dynamics in cellular automata: a tutorial
- Not just the Garden of Eden: Additional takes on cellular automata surjectivity
- A Characterization of Amenable Groups by Besicovitch Pseudodistances
- An "almost dual" to Gottschalk's Conjecture
- Balancedness and Martin-Lof randomness in cellular automata
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