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Let's say I would like to implement an algorithm.

Let's say this algorithms is patented, but its description is fully accessible.

Let's say I study and replicate it on a software of mine.

Let's say I sell this piece of software and make some money.

I don't want to know if I'm in danger, but... how could the original author discover that my (closed, maybe code-obfuscated) software is using his algorithm?

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If something is patented, by definition, its description is fully accessible since a patent's text and drawings must enable someone in the field to make add use the claimed material without undue experimentation. A patent on the hidden inner workings of something can be hard to police. Most things can be reverse engineered if the stakes are high enough and, once in court, your internal communications, etc. can be unearthed and used against you. –  George White May 12 at 15:15
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