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    AI may crack other complexity problems before P vs NP, two users suggest

    One post argues that “essentially zero direct progress” on proving P ≠ NP leaves advanced AI little to build on, unless P = NP.

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    TLDR

    Two September 11, 2026 posts suggest that separating NP from L (log space), or BPP from NEXP, might be more tractable for AI than P vs NP. One also names P versus PSPACE as a possible nearer-term target. Their skepticism about P vs NP differs: one says it will remain beyond AI’s reach, while the other considers a resolution unlikely soon, arguing that “essentially zero direct progress” on proving P ≠ NP leaves even many advanced models little to work with unless P = NP.

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    6 Sources, first seen 19d ago

    Combined views

    106.7K

    6 Sources, first seen 19d ago

    710 likes
    19d ago
    first seen 19d ago
    710 likes
    38 comments
    170 saves
    75 reposts

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    38 comments
    170 saves
    75 reposts
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    6 Sources

    @fortnowWhile P vs NP will remain out of the reach of AI, there are other complexity problems, like separating NP from L (log space) or BPP from NEXP, that might be more tractable and would still make an incredible splash.
    @aminkarbasiMy prediction: among the Millennium Prize Problems, P versus NP will be the last one solved by AI. I am very well aware of the fact that this tweet may not age well. So, watching @BooleanAnalysis is a good investment.
    @rrwilliamsI agree, P/NP seems unlikely to be resolved soon. There's been essentially zero direct progress on P!=NP, so there's not much for an advanced model (or 10k parallel advanced models) to work with unless P=NP. But I could see L/NP, BPP/NEXP, P/PSPACE, etc falling not long from now
    @_onionesqueRT @fortnow: While P vs NP will remain out of the reach of AI, there are other complexity problems, like separating NP from L (log space) o…
    @AarothBut of course this has been no obstacle to solving almost every real-world statistical leanring problem of this sort. The model of worst-case complexity is elegant but turns out to be a poor guide for what is possible (or even easy and reliable) on naturally occuring problems.

    6 Sources

    @fortnowWhile P vs NP will remain out of the reach of AI, there are other complexity problems, like separating NP from L (log space) or BPP from NEXP, that might be more tractable and would still make an incredible splash.
    @aminkarbasiMy prediction: among the Millennium Prize Problems, P versus NP will be the last one solved by AI. I am very well aware of the fact that this tweet may not age well. So, watching @BooleanAnalysis is a good investment.
    @rrwilliamsI agree, P/NP seems unlikely to be resolved soon. There's been essentially zero direct progress on P!=NP, so there's not much for an advanced model (or 10k parallel advanced models) to work with unless P=NP. But I could see L/NP, BPP/NEXP, P/PSPACE, etc falling not long from now
    @_onionesqueRT @fortnow: While P vs NP will remain out of the reach of AI, there are other complexity problems, like separating NP from L (log space) o…
    @AarothBut of course this has been no obstacle to solving almost every real-world statistical leanring problem of this sort. The model of worst-case complexity is elegant but turns out to be a poor guide for what is possible (or even easy and reliable) on naturally occuring problems.