EE 102 students! Tired of waiting for your synthesizer to finish routing? Check out this one weird trick to prove P = NP - and more - that the computer programmers down the hall DON’T want you to know!
We’re all used to the computer scientists whining. Oh, this problem is impossible even conceptually. The traveling salesman problem takes more time than there are ways to coat beach sand with all protons in the universe. My job is sooooo hard.
Now you can expose what we always knew were lies! This simple circuit, discovered by a tragically overworked student JUST LIKE YOU, solves the “NP complete” (ridiculous!) Boolean satisfiability problem not just in polynomial time, but INSTANTLY! Simply construct the instance out of gates, insert it into the circuit, and drive the input to logic high. Immediately, you can read off the necessary Boolean inputs below!
The simple construction, already obvious to most of you, relies only on basic principles: that the op amp does “whatever is necessary” to keep its differential input zero! This principle, already known to the designers of op amps, is reflected right in the name. An OPerational amp lets you compute any operation!
Order now and we’ll show you how to solve negated instances JUST AS EASILY!
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Op amps are an active, nonlinear circuit component that are nonetheless often taught in introductory EE, because they are hella useful (but not this useful). Intro classes are often oriented around passive linear components - resistors, inductors, capacitors, and sometimes transformers - so very idealized models are used.
They were taught to me like this:
an op amp puts a voltage on the output proportional to the difference in voltage of the inputs. The multiplying factor is called “open loop gain”.
the open loop gain of an ideal op amp is infinite.
therefore, to get a finite voltage out, the difference between the inputs must be zero.
So they’re usually used to equate voltages, as in a basic buffer amplifier, or bla bla they’re always used with feedback. E.g., the buffer works by putting the input on one input terminal of the amp, and connecting the amp’s output to the other input; so now the output has to equal the input.
But this is obviously impossible in general, as evidenced by this stupid circuit. It can’t possibly let you invert arbitrary functions, as evidenced by this stupid drawing.
What actually happens, as far as I can discern, is that the amplifier indeed works as an amp, but before it can reach “infinite output” it passes through every voltage in between, which (if the feedback is set up correctly) includes the output that drives the feedback input appropriately.
“If the feedback is set up correctly” implies that the correct output is actually there. In this circuit, the logic high input (positive) is inverted and compared to the initially zero feedback input, so the amp output is driven ever more negative, which of course doesn’t solve a Boolean circuit.