Yes, n-NOR is simpler and I prefer it for that reason. I was thinking of
practical implementations that already take 50 hours using 32 or 64 bit
operations. We would need to write a translator for n-NOR to C, preferably
one that can optimize by grouping bits into integer and vector operations.

On Fri, Oct 15, 2021, 5:41 PM Matt Mahoney <[email protected]> wrote:

>
>
> On Fri, Oct 15, 2021, 4:50 PM <[email protected]> wrote:
>
>> So the goal is to make a circuit (?_that is ONLY made of NOR
>> components_?) that outputs a 1 only when the input is enwik9? Hence the
>> size of said circuit is the score? How do you know if some other input ex.
>> enwik8 wouldn't pop out a 1? You'd have to feed in all possible inputs to
>> see if does, no?
>>
>
> In general, yes, unless P = NP. It's a minor variation of SAT. The best
> known solution time increases exponentially with the size of the circuit
> description.
>
> Thus, my proposal that is easier to test. (Input is 33 bit n, output is
> n'th bit of enwik9). You don't even need to specify hardware constraints
> because run time and memory only depend on the size of the circuit.
>
> It might be interesting to expand this beyond NOR gates to a more general
> hardware description language that could be implemented more efficiently on
> a computer. So you could have adders, multipliers, parallel vector logic
> operators, etc, which in principle could all be made of NOR gates. We would
> keep the requirement of a feed forward network only, with no clock,
> registers, memory, or feedback loops.
>

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