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User:Anisomorphism: Difference between revisions
→Algebraic Geometry of Computing
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Finite state machines appear in a variety of instantiations: mechanical, electronic, fluidic. The physical mechanisms involved necessitate that the design is described by differential equations, but ultimately the manipulation of abstracted "logical" states is the final goal. Thus we can describe the architecture of a general finite state machine with <math> \mathbb{Z}/2\mathbb{Z} </math> algebra (or other finite rings too). | Finite state machines appear in a variety of instantiations: mechanical, electronic, fluidic. The physical mechanisms involved necessitate that the design is described by differential equations, but ultimately the manipulation of abstracted "logical" states is the final goal. Thus we can describe the architecture of a general finite state machine with <math> \mathbb{Z}/2\mathbb{Z} </math> algebra (or other finite rings too). | ||
=== Gates === | === Gates === | ||
Typically you will see a logic gate defined by its values as a "truth table": | Typically you will see a logic gate defined by its values on all combinations of inputs as a "truth table": | ||
{| class="wikitable" style="margin:auto" | {| class="wikitable" style="margin:auto" | ||
|+ AND | |+ AND | ||
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| 1 || 1 || 1 | | 1 || 1 || 1 | ||
|} | |} | ||
And statements written with logical connectives: <math> \ | And statements written with logical connectives: <math> (x\and y)\or z = OR(AND(x,y),z) </math> | ||
== Read prototype == | == Read prototype == | ||