What are the implications if P=NP in Artificial Intelligence?

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Discussion Overview

The discussion revolves around the implications of the P=NP problem in the context of Artificial Intelligence (AI). Participants explore theoretical, practical, and philosophical aspects of what it would mean if P were to equal NP, particularly regarding creativity, problem-solving, and the future of AI development.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants argue that if P=NP, then an algorithm could solve any NP problem in polynomial time, rendering creativity and AI unnecessary for intellectual inquiries.
  • Others contend that even with P=NP, there would still be NP-hard problems not covered by NP-completeness, suggesting that creativity remains relevant.
  • A participant questions the feasibility of such an algorithm being developed in the near future and suggests that its impact on AI would be limited to certain subsets of problems, such as optimization and natural language processing.
  • Another viewpoint emphasizes that while P=NP could lead to faster computations, many AI applications focus on "good enough" solutions rather than optimal ones, indicating that the practical impact may not be as dramatic.
  • One participant humorously claims that if they were to prove P=NP and find a general algorithm, they would not publish it, hinting at the potential for personal gain over communal knowledge.

Areas of Agreement / Disagreement

Participants express a range of views on the implications of P=NP, with no consensus reached. Some believe it would diminish the need for creativity and AI, while others argue that significant challenges would remain regardless of the outcome.

Contextual Notes

Participants highlight the complexity of the implications of P=NP, noting that many assumptions and definitions are at play, and the discussion does not resolve the mathematical intricacies involved.

Gjmdp
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If it turns out that there is, indeed, an algorithm that can solve any NP problem (now also P) in polynomial type, so that P=NP, creativity would prove worthless with such algorithm. Thereby, AI will not be needed as any intellectual inquiry we would ever had could be easily solved with this algorithm. Hence, we should try to solve the P=NP problem rather than research in Artificial Intelligence. Right?
 
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Gjmdp said:
If it turns out that there is, indeed, an algorithm that can solve any NP problem (now also P) in polynomial type, so that P=NP, creativity would prove worthless with such algorithm. Thereby, AI will not be needed as any intellectual inquiry we would ever had could be easily solved with this algorithm. Hence, we should try to solve the P=NP problem rather than research in Artificial Intelligence. Right?

Not so in my opinion. First I would ask you, from which perspective do you examine the impact of (a potential) P = NP?
From a programming perspective it is a search problem And it would eliminate the pains of trial and error. Is this technologically feasible in the near future?
I don't think so but even if it is, its impact on AI will be in terms of a subset. Some problems (e.g. some optimization problems, natural language processing and a variety of others) will still be open. Surely, the impact of P = NP will be huge. Programs, computers, networks and what not, will run faster. It may also bring unforeseeable improvements at various levels and sectors but at least as I see it, it can't solve anything and everything in AI.

As a second point, I would ask what would be the impact for AI at the human level? Our brain works the way it does even with approximations and it has proven to do very well. Optimized (or even better optimal solutions) are always welcome but whether P = NP or not our brain will be needed.
 
Gjmdp said:
If it turns out that there is, indeed, an algorithm that can solve any NP problem (now also P) in polynomial type, so that P=NP, creativity would prove worthless with such algorithm.
Such math would sure turn many things upside down, but since many application of AI is not exactly about optimal, but 'good enough' responses, I think the impact on practical level would not be a really dramatic one.

Just look around: the whole NN, big data and AI stuff is about being lazy and trying to spare the effort for digging up the optimal/exact algorithms... o0)
 
Gjmdp's Title said:
What are the implications if P=NP in Artificial Intelligence?
If P=NP, and I am the first to prove that and/or find/invent a general algorithm that can exploit NP being in P, I freely promise that I will NOT publish the proof/algorithm, and I'll be careful to create a plausible fiction for how I made such a grotesquely large amount of money so fast.

 

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