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TL;DR: I am in a need of a good, precise word or an expression capturing the notion that a computer science problem P remains open (just) because it is virtually impossible to specify/define what a good solution would look like. Unfortunately, it needs to fit the semi-formal style of scientific writing.

Background: In the past, people have argued that their solution to P is the best because the outputs are human friendly. Other bunch of authors have argued that their answer to P is the best because the outputs of their solution to P make sense (kind of) even when tried on new, previously unseen inputs. And yet another school claims that their solution is the best because it considers a modification of the problem P - P' - that makes P a harder problem, and fares very well in that scenario.

My attempts:

the problem remains open mainly due to the inherent ambiguity in what is considered a "good'' solution

the problem remains open mainly due to the prevalent difficulty of specifying of what constitutes a "good" solution

the problem remains open mainly due to the inherent vagueness in the definition of successful outcome

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    The solutions lack an agreed single measure of merit?
    – Phil Sweet
    Jul 5 at 10:19
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    Multifaceted is often used for a complex/complicated problem that has many aspects and contributing factors, and that can generate multiple outcomes/arguments. Although, your own question might be multifaceted; so let me know if this word works for you.
    – ermanen
    Jul 5 at 10:39
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    The expression I would use is asking the wrong question, or barking up the wrong tree, both of which have the property of using a definite article to indicate the opposite of definiteness. Jul 5 at 15:33
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    The problem is not well posed. Jul 6 at 3:06
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    Possibly open-ended problem. Here is a definition I've found on umich.edu: "Open-ended problems are those which have many solutions or no solutions for the problem as defined." If one wants to be more concrete, insoluble can be used, "due to its insolubility".
    – ermanen
    Jul 6 at 8:37

1 Answer 1

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Your attempts are actually quite accurate in describing your situation. I find your 2nd example best.

I might suggest:

According to Collins Dictionary:

nigh impossible: Something that is impossible cannot be done or cannot happen

the problem is mainly open due to it being nigh impossible to define what constitutes a good solution

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  • Thanks. But it does change the meaning I am afraid. The problem itself does admit a few solutions, but judging their quality and definitiveness is difficult
    – user35443
    Jul 6 at 7:23
  • Perhaps due to it being nigh impossible to define what constitutes a good solution would fly?
    – user35443
    Jul 6 at 7:23
  • Yes that would work @user35443
    – DialFrost
    Jul 6 at 7:38

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