Rice’s Theorem for μ-Limit Sets of Cellular Automata
Cellular automata are a parallel and synchronous computing model, made of infinitely many finite automata updating according to the same local rule. Rice’s theorem states that any nontrivial property over computable functions is undecidable. It has been adapted by Kari to limit sets of cellular automata , that is the set of configurations that can be reached arbitrarily late. This paper proves a new Rice theorem for μ-limit sets, which are sets of configurations often reached arbitrarily late.
KeywordsCellular Automaton Computable Function Local Rule Permanent State Bruijn Sequence
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