I wonder whether it is necessary to use third-person singulars for the verbs in the step-form algorithm description, which I explain now.
The first version is without third-person singulars.
The algorithm A has the following steps:
- Compute B=f(A).
- Check whether g(B)=1.
- Output h(B).
The second version uses third-person singulars.
The algorithm A has the following steps:
- Computes B=f(A).
- Checks whether g(B)=1.
- Outputs h(B).
Which one is more grammatically correct?
In my experience, we invariably use the plain form (compute, check, output). I imagine that this is because the algorithm is essentially a set of instructions, similar to those for a laboratory experiment, a recipe, etc., so it uses the imperative mood with an implied second-person subject; and indeed, although we often think of algorithms as being executed by computer programs, they are often executed by humans, and have been for millennia. (And that's not just from a modern perspective; the very word algorithm long predates computing machines.)
That said, if you prefer, you can probably just think of them as bare infinitive phrases; I can't imagine any algorithm steps being negated (imperative "don't X" vs. bare infinitive "not X") or referring directly to the reader ("While holding the array A in your left hand, slowly shuffle array B into it"), so for all intents and purposes that should be equivalent.
