Circuits via topoi

07/18/2018

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by   Arnaud Spiwack, et al.

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Leveraging topos theory a semantics can be given to sequential circuits where time-sensitive gates, such as unit delay, are treated uniformly with combinational gates. Both kinds of gates are functions in a particular topos: the topos of presheaves over the natural ordering of N. This is used to show that sequential circuits validate the equational theory of traced categories.