Recursive Calls to a Logic Block

I haven’t tried but would like to know if we can call a logic bock recursively.

Yes, you are able to call a LB recursively, same way as calling any other LBs.

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Worth noting that there is a call stack depth limit that’s in place to prevent infinite loops (see What does it mean when I run into a "Excessive logic block call depth." error?).
Recursion is definitely allowed, but if you have a scenario where you would perform it too many times in a row, you’ll get that error. In such cases, there are always different ways to architect a solution that will prevent the call stack from getting too deep.

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Thanks for the information.