This question explains the singular and plural of performance depends on the contex. One person answers that regarding algorithms, it's always singular, but perhaps other people disagreed. Here's the passage.
In the classical model of computation, the state-of-the-art in factoring is a composition of four algorithms. Due to their performance, they are executed in a specific order in the search for a non-trivial factor of the composite number one wishes to factor.
Should it be "due to their performances"?
What makes it difficult for me in this case is the presence of "their". So I'm not sure this passage can be put in the singular as Peter Shor recommends.
Wikipedia uses the plural in one case, but that example doesn't clarify what should be done in this case.
In this context, I'm inclined to say it should be singular because the performance of algorithms is in many ways a measure of how successful they are, determining the context, but I'm not sure. What would you say is the context here of this case?
The text could be written to "Due to their complexity classes, [...]" and then plural would be a necessity. But I'm in the interested in the question asked, not in how it could be rewritten.
