For SAT problems with 10 variables and 200 clauses, sometimes outputted UNSAT because it couldn't find any satisfying assignment, and it would take a lot more time to find one, which is logically sound. I don't consider this as bad reasoning as it is about performance. So I tried it with only 100 clauses and it successfully found valid assignments.
This makes sense. These keys were designed as project identifiers for billing, and can be further restricted with (bypassable) controls like HTTP referer allow-listing. They were not designed as authentication credentials. ,这一点在同城约会中也有详细论述
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