[FOM] Gordeev and NP = PSPACE again

[Joe Shipman]

That is a welcome development. Is your completion of the proof independent of his? Or do you use some of the new constructions in his new preprint?

— JS

Sent from my iPhone

> On Jul 31, 2019, at 1:53 AM, Edward Hermann Haeusler <edward.haeusler at gmail.com> wrote:
> 
> Dear Timothy,
> 
> As prof. Gordeev knows, we took slightly different directions in order to proof our result. In order to avoid incomplete versions, I and my students, are formalizing  our version in LEAN. Only after each relevant part is formalized and checked there will be an article published it in arxiv......
> 
> Best regards,
> 
> Hermann
> 
> 
> 
>> Em ter, 30 de jul de 2019 às 7:02 PM, Lew Gordeew <lew.gordeew at uni-tuebingen.de> escreveu:
>> Dear Tim,
>> 
>> It's easy. Proof outline shown in preprint [2] turned out to be  
>> incomplete, although we stand by its general roadmap. First verified  
>> part of [2] was published in an authorized paper [3]. Second, final  
>> part is elaborated in my new preprint [1] (hopefully it is complete  
>> and correct). By the way, it is the abstract of [1] (not [2]) that  
>> says "We upgrade [3] to a complete proof of the conjecture NP =  
>> PSPACE." Thus "[1] does not cite [2], but cites only [3]."
>> 
>> Best regards,
>> Lev
>> 
>> 
>> Zitat von "Timothy Y. Chow" <tchow at math.princeton.edu>:
>> 
>> > Lev Gordeev has recently posted an arXiv preprint purporting to  
>> > prove that NP = PSPACE.
>> >
>> >   [1]  Lev Gordeev, Proof Compression and NP Versus PSPACE, Part 2,
>> >        https://arxiv.org/abs/1907.03858
>> >
>> > FOM readers may recall that Gordeev and Haeusler posted an arXiv  
>> > preprint back in 2016, also claiming to give a proof that NP = PSPACE.
>> >
>> >   [2]  Lew Gordeev and Edward Hermann Haeusler, NP vs PSPACE,
>> >        https://arxiv.org/abs/1609.09562
>> >
>> > There was some discussion of [2] on FOM back in October 2016:
>> >
>> >   https://cs.nyu.edu/pipermail/fom/2016-October/thread.html
>> >
>> > To summarize the discussion, some people pointed out that what  
>> > Gordeev and Haeusler were claiming in [2] seemed to contradict known  
>> > results, but Gordeev and Haeusler replied that in fact there was no  
>> > contradiction. Also, Richard Zach said that several crucial points  
>> > in [2] were unclear.
>> >
>> > In addition, there was an amusing interchange on Scott Aaronson's  
>> > blog, where he gave 500:1 odds against [2] being correct, betting  
>> > with someone using the pseudonym "Polymath."  Polymath said, "I'm  
>> > sure the correctness of their proof will be settled one way or  
>> > another within 2 or 3 months," but I have no idea whether Polymath  
>> > and Aaronson actually settled their bet.
>> >
>> > https://www.scottaaronson.com/blog/?p=2925
>> >
>> > Skimming [1] briefly, I was surprised to find that [1] makes no  
>> > mention of [2].  Instead, [1] refers to a recently published paper  
>> > by Gordeev and Haeusler:
>> >
>> >   [3] L. Gordeev and E. H. Haeusler, Proof Compression and NP Versus
>> >       PSPACE, Studia Logica 107 (2019), 55-83.
>> >
>> > [3] does not claim to prove that NP = PSPACE.  The abstract of [2]  
>> > says, "We upgrade [3] to a complete proof of the conjecture NP =  
>> > PSPACE."
>> >
>> > Since [2] has not been withdrawn from the arXiv, one might suppose  
>> > that the authors stand by its correctness, but in that case it is  
>> > curious that
>> >
>> > a. the published paper [3], whose abstract and content superficially  
>> > look a lot like [2], conspicuously avoids claiming to prove that NP  
>> > = PSPACE, and
>> >
>> > b. as already mentioned, [1] does not cite [2], but cites only [3].
>> >
>> > Note also that [1] is authored only by Gordeev and not by Haeusler.
>> >
>> > I believe that Gordeev and Haeusler subscribe to FOM, so perhaps  
>> > they can clarify whether they still maintain that [2] provides a  
>> > complete and correct proof that NP = PSPACE.
>> >
>> > Tim
>> > _______________________________________________
>> > FOM mailing list
>> > FOM at cs.nyu.edu
>> > https://cs.nyu.edu/mailman/listinfo/fom
>> 
>> 
>> 
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> -- 
> Edward Hermann Haeusler
> Associate Professor 
> Department of Informatics
> PUC-Rio
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