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And in practice if there are many simple rules that are universal they cannot all be related by simple encodings.
David Hilbert ): Mathematics studies formal rules that have no intrinsic meaning, but are relevant because of their applications or history.
• Platonism (e.g.
(As discussed above, any cellular automaton rule can be represented as an appropriate combination of bitwise functions.)
History [of cyclic tag systems]
Cyclic tag systems were studied by Matthew Cook in 1994 in connection with working on the rule 110 cellular automaton for this book.
Periods in rule 37R
With a system of size n , the maximum possible repetition period is 2 2n .
With modus ponens as the rule of inference, the shortest single-axiom system that works is known to be {(a ∘ b) ∘ ((c ∘ b) ∘ (a ∘ c))} .
Nand tautologies
At each step every possible transformation rule in the axioms is applied wherever it can.
(Iterating the related function BitXor[i, 2i] yields numbers whose digit sequences correspond to the rule 60 cellular automaton).
And, as it happens, in the mid-1980s I tried hard, though at the time without much success, to use updating rules for networks as the basis for a new kind of programming language intended for massively parallel computers.
Implementation [of network properties]
Networks are conveniently represented by assigning a number to each node, then having lists of rules which specify what nodes the connection from a particular node go to.
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