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The logic of MOSFET logic

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Metal-oxide semiconductor field-effect transistors (MOSFET) are most commonly used in integrated circuits and microprocessors, especially using the complementary symmetry style (CMOS). When used in saturated mode the behaviour of MOSFET is digital in nature. Boolean circuits, which implement a two-valued logic, have been extensively studied. Somewhat surprisingly, “MOSFET logic” (a colloquial term for MOSFET digital circuits) has not been mathematically studied, as far as I could tell. MOSFET logic is interesting both practically, because it is the underlying logic of Boolean logic, and mathematically, because it refines Boolean logic with new logical values (Z — “high impedance” and X — “illegal value”) and structural connectives (e.g. joining two wires). In this preliminary work we will look in some detail at the simpler case of combinatorial MOSFET , from categorical specification to a rewriting system to use in simulation. We will conclude by discussing some of the challenges and potential rewards for a comprehensive mathematical (categorical, logical, rewriting) understanding of MOSFET circuits with feedback.

This talk is part of the CAS Talks series.

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