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Is it possible to make an arbitrary logic circuit using only single bit gates (Single input, single output) and some multiple bit gates (n bits in m bits out where n and m are any integers) which must be in a fixed position.

Or to ask the question another way:

Presume there exists a circuit which has some multiple bit gates in some fixed locations and many empty spaces where other gates may be inserted.

Would I be able to make an arbitrary program if I choose to only put in single input, single output logic gates in these empty places?

Would I require that the original circuit with fixed gates is infinitely large or exponentially bigger than the normal circuit for the same piece of logic?

Thanks in advance

Josh Ketts
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1 Answers1

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Responding to myself incase others read this - Yes, this is universal.

Any 2-bit-input/1-bit-output gate may be constructed by using two 1-bit-input/1-bit-output gates in two predefined places.

From here universality follows.

Josh Ketts
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