Open book, sure. But you don't even need a computer for that.

I make a point of only using references that are either available for free online or through our university’s library subscriptions. These are all electronic. My open book exam became an open computer exam when I realized students were printing hundreds of pages just for a 3-hour exam. This semester I’m switching to no-computer, bring your own printed cheat-sheet for the exam.

Except that the physical book isn't the way people lookup facts these days.

The open book test is purposes is to not have to know all facts (formulas) but proving how to find them and how to apply them. (Finding is part of it as the more you look, the less time you got to use it, thus there is an optimisation problem which things to remember and which to look up)

In modern times you wouldn't look those up in a book, thus other research techniques are required to deal with real life (which advanced certifications should prove)

And even if you are allowed to use a computer, you cannot use internet (and should not be hard to prevent that).