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I noticed that AND, OR, NOT those three logic gates are Functionally Complete, it means I can represent any trues table only by those three gates.

So, I want to know whether I can represent any computable function only by those three gates ?

Yachao Zhu
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  • Related: http://stackoverflow.com/questions/4908893/what-logic-gates-are-required-for-turing-completeness?rq=1 – Thilo Oct 31 '16 at 02:37
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    I saw that question before ask this but still I don't understand well. A Turing machine may halt or not in a particular input but a combinational(not sequential) logic circuit always gives an output in a particular input. You may not agree with my point on combinational circuit but a combinational circuit is just a deterministic system so I can evaluate step by step in a input until it gives an output, in other words, there is no loops in a combinational circuit, I think. Any way, thx! – Yachao Zhu Oct 31 '16 at 02:59
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    I'm voting to close this question as off-topic because it belongs on cs.stackexchange.com but would be closed as a trivial duplicate there. – Joshua Oct 31 '16 at 03:02
  • FWIW: The answer to "I want to know whether I can represent any computable function only by those three gates" is No. Truth tables cannot represent partial functions and thus are not Turing complete (since TC is equivalent to Partial Recursive Functions). They are not even Primitive recursive since S (the successor) cannot be represented with a finite number of bits. IIRC they should be as powerful as DFA. – Margaret Bloom Nov 04 '16 at 14:34

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