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I am writing a scientific paper, and I started the first sentence of one paragraph as below:

Many algorithms are available, depending on problems to be solved.

Someone told me that I need to add the before the word problems. However, I didn't mean a specific problem here. I don't think I need the. Do I need it? Could you please explain?

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The use of the definite article "the" communicates that you are referencing specifically identified problems. Because the algorithms are dependent on specific problems, you would need to identify the problems in order to determine the algorithms available, thus indicating that you are referring to a specific, identified subset of all possible problems.

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