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• Curtis–Hedlund–Lyndon_theorem abstract "The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund credited Curtis and Lyndon as co-discoverers. It has been called \"one of the fundamental results in symbolic dynamics\".The theorem states that a function from a shift space to itself represents the transition function of a one-dimensional cellular automaton if and only if it is continuous (with respect to the Cantor topology) and equivariant (with respect to the shift map). More generally, it asserts that the morphisms between any two shift spaces (i.e., continuous mappings that commute with the shift) are exactly those mappings which can be defined uniformly by a local rule.The version of the theorem in Hedlund's paper applied only to one-dimensional finite automata, but a generalization to higher dimensional integer lattices was soon afterwards published by Richardson (1972), and it can be even further generalized from lattices to discrete groups. One important consequence of the theorem is that, for reversible cellular automata, the reverse dynamics of the automaton can also be described by a cellular automaton.".
• Curtis–Hedlund–Lyndon_theorem wikiPageID "18903091".
• Curtis–Hedlund–Lyndon_theorem wikiPageLength "10943".
• Curtis–Hedlund–Lyndon_theorem wikiPageOutDegree "38".
• Curtis–Hedlund–Lyndon_theorem wikiPageRevisionID "637156872".
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Alphabet_(formal_languages).
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Atlas_(topology).
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Cantor_space.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Category:Articles_containing_proofs.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Category:Cellular_automata.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Category:Symbolic_dynamics.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Category:Theorems_in_discrete_mathematics.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Cellular_automaton.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Characterization_(mathematics).
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Compact_space.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Continuous_function.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Cover_(topology).
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Discrete_group.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Equivariant_map.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Function_(mathematics).
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Group_action.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Gustav_A._Hedlund.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Integer.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Integer_lattice.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Morphism.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Morton_L._Curtis.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Reversible_cellular_automaton.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Roger_Lyndon.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Sequence.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Shift_operator.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Shift_space.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Surjunctive_group.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Symbolic_dynamics.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Topological_space.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLink Tychonoffs_theorem.
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLinkText "Curtis–Hedlund–Lyndon theorem".
• Curtis–Hedlund–Lyndon_theorem wikiPageWikiLinkText "translation-invariant and continuous".
• Curtis–Hedlund–Lyndon_theorem wikiPageUsesTemplate Template:Harvtxt.
• Curtis–Hedlund–Lyndon_theorem wikiPageUsesTemplate Template:Math.
• Curtis–Hedlund–Lyndon_theorem wikiPageUsesTemplate Template:Mvar.
• Curtis–Hedlund–Lyndon_theorem wikiPageUsesTemplate Template:Reflist.
• Curtis–Hedlund–Lyndon_theorem subject Category:Articles_containing_proofs.
• Curtis–Hedlund–Lyndon_theorem subject Category:Cellular_automata.
• Curtis–Hedlund–Lyndon_theorem subject Category:Symbolic_dynamics.
• Curtis–Hedlund–Lyndon_theorem subject Category:Theorems_in_discrete_mathematics.
• Curtis–Hedlund–Lyndon_theorem hypernym Characterization.
• Curtis–Hedlund–Lyndon_theorem type Dynamic.
• Curtis–Hedlund–Lyndon_theorem type Proof.
• Curtis–Hedlund–Lyndon_theorem type Redirect.
• Curtis–Hedlund–Lyndon_theorem type Theorem.
• Curtis–Hedlund–Lyndon_theorem comment "The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund credited Curtis and Lyndon as co-discoverers.".
• Curtis–Hedlund–Lyndon_theorem label "Curtis–Hedlund–Lyndon theorem".
• Curtis–Hedlund–Lyndon_theorem sameAs Q5195996.
• Curtis–Hedlund–Lyndon_theorem sameAs m.04jn_8y.
• Curtis–Hedlund–Lyndon_theorem sameAs Q5195996.
• Curtis–Hedlund–Lyndon_theorem wasDerivedFrom Curtis–Hedlund–Lyndon_theorem?oldid=637156872.
• Curtis–Hedlund–Lyndon_theorem isPrimaryTopicOf Curtis–Hedlund–Lyndon_theorem.