# Tag Info

Accepted

### What's the status of Babai's Graph isomorphism result?

Aggregating comments by Thomas Klimpel, Sasho Nikolov and Mohammad Al-Turkistany into a community answer: The correction (and hence the quasi-polynomial result) was immediately supported by Harald ...
Accepted

### Examples of algorithms and proofs that seem correct, but aren't

2D local maximum input: 2-dimensional $n \times n$ array $A$ output: a local maximum -- a pair $(i,j)$ such that $A[i,j]$ has no neighboring cell in the array that contains a strictly larger value. ...
• 10.8k

### Possible to do Complexity theory with only counting and Pigeonhole

If you are looking for non-pigeon-hole type arguments, then there is good news: they exist! The pigeon-hole principle is a certain template for proof by contradiction. There are concepts in TCS which ...
• 2,024

• 11.5k
Accepted

### Conversion between NP certificates

For general $L\in\mathrm{NP}$, this is equivalent to $\mathrm{FP=TFNP}$, hence likely false: On the one hand, if $V$ and $V'$ are verifiers of $L$, then “given $x$ and $u$ such that $V(x,u)$, find $u'$...
• 17.9k

### Examples of the value of proofs for algorithms

Here is a natural problem from graph theory where the proof and the algorithm are closely intertwined. In my view, one can discover this algorithm only via thinking about the proof and the algorithm "...
• 11.4k

### Proof of Levenshtein distance

I looked into this last year while teaching. The other answers, including Prof. Erickson's excellent book, feel incomplete, because they handwave a step along the lines of "there is an optimal ...
• 7,615

### Where is the quote "Informal proofs are algorithms, formal proofs are code" from?

He doesn't cite any references for it and Google doesn't return any results so I don't think he is really quoting from anywhere. The idea that a proof is a "construction" (a term in intuitionistic/...
• 21.7k
Accepted

### Complexity of counting the number of edge covers of a graph

After some more literature search, it appears that the complexity of counting the edge covers in a graph was shown to be #P-complete in bordewich2008path, Appendix A.1. (This assumes arbitrary graphs ...
• 9,547