# Tag Info

Accepted

### Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

As noted here before, Tardos' example clearly refutes the proof; it gives a monotone function, which agrees with CLIQUE on T0 and T1, but which lies in P. This would not be possible if the proof were ...
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### Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

I am familiar with Alexander Razborov whose previous work is extremely crucial and serves as a foundation for Blum's proof. I had the good luck of meeting him today and wasted no time in asking for ...
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### Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

This is posted as community answer because (a) it's not my own words, but a citation from Luca Trevisan on a social media platform or from other people with no CSTheory.SE account; and (b) anyone ...

### Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

The correctness of the claimed proof is being discussed at Luca Trevisan's blog: https://lucatrevisan.wordpress.com/2017/08/15/on-norbert-blums-claimed-proof-that-p-does-not-equal-np/ In particular "...
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### Are there any hard instances of 3-SAT when the clauses can only use literals that are "nearby" each other?

No. If the 3-SAT instance has $m$ clauses, then you can test satisfiability in $O(m 2^N)$ time. Since $N$ is a fixed constant, this is a polynomial-time algorithm that solves all instances of your ...
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Accepted

### Did "Where the really hard problems are" hold up? What are current ideas on the subject?

Here is a rough summary of the status based on a presentation given by Vardi at a Workshop on Finite and Algorithmic Model Theory (2012): It was observed that hard instances lie at the phase ...

### Is Norbert Blum's 2017 proof that $P \ne NP$ correct?

Gustav Nordh commented on by Theorem 5 (page 29). Specifically, the function $$(x\lor y) \land (\lnot x \lor y) \land (x \lor \lnot y)$$ computes the function which is $1$ only if $x$ and $y$ are ...
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### Tardos Function Counterexample to Blum's $P\neq NP$ Claim

so these remarks imply that the Tardos function $f$ is the same as CLIQUE. Short answer - NO. It is only a *monotone* "clique-like": accepts all $k$-cliques, and rejects all complete $(k-1)$-...
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### To which complexity class does this language belong?

(as pointed out by Robin the problem is in DP...) ...and it is also DP-complete. In fact, Jörg Rothe has shown that this even holds for fixed k=4: Jörg Rothe: Exact complexity of Exact-Four-...
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Accepted

• 13.7k