Are 'complexity' and 'performance' countable or noncountable?

Question

First of all, I am sorry to ask a question that is worth asking a lot of people, but I could not find an answer that was right for me, so I am posting a new question.

In many scientific journals, e.g., papers published by IEEE, the words 'complexity' and 'performance' appear very frequently. I also want to use these two words in my paper, but I am wondering whether to consider them as countable nouns or uncountable nouns.

According to many existing papers (searchable in google scholar), Sometimes they are used as being uncountable (e.g., We develop a blah-blah-blah scheme with low computational complexity; The performance of A and B schemes is blah-blah-blah.), sometime as being countable (e.g., We develop a blah-blah-blah scheme with a low computational complexity; The performances of A and B schemes are blah-blah-blah).

On the other hand, according to the Merriam-webster dictionary, the word 'performance' is defined as

Performance: how well someone or something functions, works, etc. : how well someone or something performs. (and there are both examples for 'count' and 'noncount')

Can I decide whether to use the above two words as a countable noun or a noncountable noun??? For example,

• 'To this end, we develop a heuristic algorithm with a low computational complexity.' vs 'To this end, we develop a heuristic algorithm with low computational complexity.'
• 'The algorithms developed in [3] and [4] have very high computational complexities.' vs 'The algorithms developed in [3] and [4] have very high computational complexity.'
• 'the performance of our proposed algorithm is better than those of other baseline algorithms.' vs 'the performance of our proposed algorithm is better than that of other baseline algorithms.'
• 'We compare the performances of our algorithm and the other baseline algorithms.' vs 'We compare the performance of our algorithm and the other baseline algorithms.'

Answer 1

The short answer is that for all your examples, you should use both complexity and performance as uncountable nouns.

You should be aware that performance has more than one meaning. It can be countable:

• The actors gave a good performance last night.

But in your intended meaning, it is uncountable. (The same might apply to complexity, but it's more obvious with performance.)

Remember that many writers in the IEEE journals will be non-natives, so it's a bad idea to use them as a reference for written English. (Editors and reviewers often let poor grammar slide; they don't have time to catch everything.)