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- We prove by induction on the depth that the circuit can be computed using at most 2d + 2d 1 +... + 1 = 2d+1 1 gates. When the depth d = 0, the circuit must just output the value of a variable, and so has size at most 1. When d > 1, consider the output gate. This gate has two gates that feed into it, each of depth at most d 1.
homes.cs.washington.edu/~anuprao/pubs/431/lecture2.pdf
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Mar 3, 2013 · Theoretically speaking, an infinite number of NAND (inverted AND) logic gates can be used to build a Turing machine. This is because NAND and NOR are the universal logic gates. In the real world, one can never build a Turing complete machine because infinite memory does not exist.
Sep 3, 2019 · So using the non-infinite Turing machine definition (*), whatever that is, is there a known lower bound on the number of 2-input binary gates needed to produce a Turing complete computer? Or a reasonable guess or a minimum among known current published existing example implementations?
A Turing machine is a finite automaton equipped with an infinite tape as its memory. The tape begins with the input to the machine written on it, surrounded by infinitely many blank cells. The machine has a tape head that can read and write a single memory cell at a time.
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Turing machines can perform many operations on lists: Concatenate two lists. Reverse a list. Sort a list. Find the maximum element of a list. And a whole lot more!
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The example of trans-Turing systems, let alone evolution, frees us from the constraints of strong artificial intelligence, that mind must be based on networks of classical physics logic...
function on nvariables can be computed using around 2n gates. Do we really need that many? It turns out the answer is yes, you need exponentially many gates. I’m not going to go into the proof in detail, but the basic idea is that you can count the number of Boolean functions on nvariables, and the number of Boolean
Because of this, the number of Turing machines is countable. That is, we can “flatten” each machine into one finite-length string that describes it, and we can place these strings into a one-to-one association with integers, just as we can with rational numbers.
