#GhicaKayeSprunger-4
"Larger circuits can be constructed out of smaller circuits in three ways.
•..‘in parallel’[:] inputs and outputs are..placed side-by-side
•[‘inseries’][:] outputs of one circuit can be fed into the inputs of the next circuit[:] the resulting circuit
>
"Larger circuits can be constructed out of smaller circuits in three ways.
•..‘in parallel’[:] inputs and outputs are..placed side-by-side
•[‘inseries’][:] outputs of one circuit can be fed into the inputs of the next circuit[:] the resulting circuit
>
>has the inputs of the first circuit and the outputs of the second
•[‘#feedback’]: some of the outputs of a circuit can be fed back as its own input.
Using these three forms of #composition, circuits of billions of elementary components can be created using a very small number>
•[‘#feedback’]: some of the outputs of a circuit can be fed back as its own input.
Using these three forms of #composition, circuits of billions of elementary components can be created using a very small number>
>of basic gates; circuits that control our #computers, mobile #phones, or #car[-]engines.
And yet ,surprisingly, the semantics of such circuits is not perfectly understood, in a sense which will be made clear immediately.
>
And yet ,surprisingly, the semantics of such circuits is not perfectly understood, in a sense which will be made clear immediately.
>
>
The three forms of composition..correspond to..
#SymmetricTracedMonoidalCategories(STMCs).
Moreover, sequential circuits can
•copy values (by forking a wire)
•discard [values] (by capping.. a wire)
which confers the additional categorical structure of a Cartesian product.>
The three forms of composition..correspond to..
#SymmetricTracedMonoidalCategories(STMCs).
Moreover, sequential circuits can
•copy values (by forking a wire)
•discard [values] (by capping.. a wire)
which confers the additional categorical structure of a Cartesian product.>
• • •
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