Score:0

Perp notation question

us flag

What does the symbol $\perp$ mean? I saw this on a paper where some entity outputs $\perp$.

kelalaka avatar
in flag
Halt, stop there!
Score:3
ng flag

I've seen it used to denote 'nil', e.g. as a return value by some entity to indicate that it has nothing to return, or as a placeholder for a value which will be instantiated at a later time.

One example to see it used this way would be the Introduction to Reliable and Secure Distributed Programming textbook, where the authors use it to indicate uninitialized values and error conditions, as mentioned in the comments.

But it's speculation unless you can provide some context.

Chito Miranda avatar
us flag
My speculation is it denotes that an entity just outputs "garbage" but I am not sure. Returning nothing makes sense too but are there any other situation that $\perp$ is used to mean something else?
cn flag
It's also often used to indicate an error.
Mark avatar
ng flag
Its worth mentioning that $\perp$ is often a *distinguished* error symbol. So the algorithm is not only turning in an answer that is incorrect, but one that it *knows* it is incorrect.
meshcollider avatar
gb flag
It is also sometimes used to represent than an algorithm did not terminate - for example, in [haskell](https://wiki.haskell.org/Bottom). I have also seen it be used to represent "False", and Top (⊤) to represent "True" (this is their meaning in [logic](https://en.wikipedia.org/wiki/List_of_logic_symbols)). Context is everything.
Chito Miranda avatar
us flag
I just saw in Goldreich's Foundations of Cryptography book Volume 2, page 616 that $\perp$ denotes a special error symbol and in addition, $\lambda$ denotes the empty string.
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