Added random tests.

The debug format wasn't my choice, it was taken from the website referenced in the description which is why I have used that format.

I must admit I do neglect the description and focus on the code, something I could improve on I guess...

Thanks for your quick response. I was thrown by the [A1->B1,A2->B2...] debug format, which seems a non-standard way of enumerating a continuous array. How about just the usual [B1,B2...] or JSON-ish [A1:B1, A2:B2...]? I took your example [0->1] to mean [old->new] instead of [index->value], but perhaps I should have read the test cases more carefully before starting.
As for the output, the reference to (global?) Output is obscure, especially when conflating the meaning of "parameter" and "property". And the run-on sentences are unnecessary, distracting, and easily fixed, making it seem like basic proofreading was neglected.

I'm sorry my strength isn't description writing or explaining, I prefer to give examples within the test cases. As for the detail regaring the debug I do state that it must be an array representation of the tape which is why I have more tests in the example test case section so it's easier to understand?

The vast majority of work here is simply trying to understand the grossly imprecise description of output behavior.
This is sloppy writing:

The output expected for this kata will be an object this
object will be predefined in the solution called Output It
takes two parameters: output and debug the output must be a
number.

Say what you mean: the interpreter instance should have output and debug properties (not "parameters")!
Your only detail regarding debug is one example: 0->1, which could be interpreted as an intial zero incrementing to a one. Please verbalize more carefully and add some additional examples.

I agree it is missing a tag saying performance or something.

The beast test is easily solvable by using the right data structure. Take a look at Unnamed's solution, it's simple and gets the job done, no fancy algorithm or optimization there.

You are absolutely correct. Thank you. I've made the correction.

I must object to this:
An exclusive disjunction is typically repsented (sic) by "^" ...
Some specialized contexts (e.g. bitwise operator in some languages) use that symbol, but typically '^' means conjunction and exclusive disjunction (XOR) is represented with another symbol (⊻ or ⊕). This repurposing of '^' is confusing and unnecessary.

I like this a lot, but its tags are deceptive: the real challenge here is getting past the "beast" test, which requires thinking about algorithmic complexity/efficiency, rather than simple string/array fundamentals. I think it deserves a couple of tags in that direction-- perhaps "algorithms"?

Looks better now, thanks for updating.