While I understand why USA PATRIOT is a contrived acronym, I don't understand if CAPTCHA should be considered a contrived acronym.
Is CAPTCHA a contrived acronym? Why?
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CAPTCHA is homophonous to capture, and thus it is a contrived acronym, as described on Wikipedia. As to why it is a contrived acronym, it is the goal of the CAPTCHA system to capture bots trying to pass as human beings, in order to prevent them from doing certain actions.
The term CAPTCHA (for Completely Automated Public Turing Test To Tell Computers and Humans Apart) was coined in 2000 by Luis von Ahn, Manuel Blum, Nicholas Hopper and John Langford of Carnegie Mellon University.
Since CAPTCHA it is pronounced like a normal word it is an acronym, and not an initialism like e.g. IBM.
To answer the question:
A contrived acronym is one deliberately designed to be especially apt for the thing being named (by having a dual meaning or by borrowing the positive connotations of an existing word). Some examples of contrived acronyms are USA PATRIOT, CAN SPAM, CAPTCHA and ACT UP.