Questions tagged [proofs]

Used for questions about existing or possible proofs of a specific theorem or conjecture

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96 votes
9 answers
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What would it mean to disprove Church-Turing thesis?

Sorry for the catchy title. I want to understand, what should one have to do to disprove the Church-Turing thesis? Somewhere I read it's mathematically impossible to do it! Why? Turing, Rosser etc ...
user avatar
46 votes
4 answers
4k views

Are there any proofs the undecidability of the halting problem that does not depend on self-referencing or diagonalization ?

This is a question related to this one. Putting it again in a much simpler form after a lot of discussion there, that it felt like a totally different question. The classical proof of the ...
Mohammad Alaggan's user avatar
57 votes
18 answers
2k views

Where and how did computers help prove a theorem?

The purposes of this question is to collect examples from theoretical computer science where the systematic use of computers was helpful in building a conjecture that lead to a theorem, falsifying a ...
25 votes
4 answers
3k views

Proofs, Barriers and P vs NP

It is well known that any proof resolving the P vs NP question must overcome relativization, natural proofs and algebrization barriers. The following diagram partitions the "proof space" into ...
Shiva Kintali's user avatar
51 votes
8 answers
5k views

Are there non-constructive algorithm existence proofs?

I remember I might have encountered references to problems that have been proven to be solvable with a particular complexity, but with no known algorithm to actually reach this complexity. I struggle ...
jkff's user avatar
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29 votes
4 answers
5k views

Implications of unprovability of $P\neq NP$

I was reading "Is P Versus NP Formally Independent?" but I got puzzled. It is widely believed in complexity theory that $\mathsf{P} \neq \mathsf{NP}$. My question is about what if this is ...
karthik's user avatar
  • 407
16 votes
2 answers
1k views

Complexity of counting the number of edge covers of a graph

An edge cover is a subset of edges of a graph such that every vertex of the graph is adjacent to at least one edge of the cover. The following two papers say that counting edge covers is #P-complete: ...
a3nm's user avatar
  • 9,232
13 votes
1 answer
1k views

Correctness proofs of classic Paxos and Fast Paxos

I am reading the "Fast Paxos" paper by Leslie Lamport and get stuck with the correctness proofs of both classic Paxos and Fast Paxos. For consistency, the value $v$ picked by the coordinator in phase ...
hengxin's user avatar
  • 2,329
2 votes
2 answers
2k views

Is there an alternative proof of the TM Halting Problem other than the "standard" one? [closed]

I'm wondering if anyone is aware of a proof of the Halting Problem that is not just a permutation of the "standard" proof. Since there are so many formulations of this proof, rather than pick a ...
johne's user avatar
  • 227
1 vote
1 answer
334 views

in SAT resolution proofs, are all DAGs possible? [closed]

these are some probably very hard but possibly significant and deep questions related to an unusual but intriguing possible "recursive" construction/formulation in SAT, with some important "structure" ...
vzn's user avatar
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29 votes
1 answer
5k views

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

It's been over a year since his January 2017 retraction and correction. Is there news? If not is this normal for validation to take this long? I would expect it would get plenty of attention. Has ...
Meir Maor's user avatar
  • 434
27 votes
5 answers
946 views

Quantum proofs of classical theorems

I'm interested in examples of problems where a theorem which seemingly has nothing to do with quantum mechanics/information (e.g. states something about purely classical objects) can nevertheless be ...
Marcin Kotowski's user avatar
15 votes
1 answer
1k views

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

In my intro to programming course, we're learning about the Initialization-Maintenance-Termination method of proving an algorithm does what we expect it to. But we've only had to prove that an ...
Marin's user avatar
  • 153
13 votes
4 answers
4k views

Proof of Levenshtein distance

In the article Levenshtein distance Wikipedia says about the proof of invariant that: This proof fails to validate that the number placed in d[i,j] is in fact minimal; this is more difficult to ...
Nutel's user avatar
  • 381
11 votes
3 answers
811 views

Where do I turn for help with research/publishing?

I have been developing a SAT algorithm for a while, and have reached a point where I'd like to share it. I don't know many people in computer science, and I'm not sure exactly where to turn. I'm ...
Matt Groff's user avatar
  • 2,100
7 votes
2 answers
777 views

Proof Strategies on P versus BPP

Typically to show $P=NP$, one has to show an NP complete problem has a polynomial time solution and to show $P\neq NP$, has to show an NP complete problem has superpolynomial lower bound. These are ...
Turbo's user avatar
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4 votes
1 answer
498 views

Proof that the graph optimization problem is NP-hard

I'm trying to prove that the following optimization problem is NP-hard: Given a graph $G=(V,E)$, non-negative vertex weight functions $w(v)$ and $s(v)$, and a non-negative edge weight function $t(u,v)...
marszall87's user avatar
3 votes
3 answers
1k views

What's wrong with this proof that NP=Co-NP implies NP=PSPACE

Below is a short informal proof that NP=co-NP implies NP=PSPACE. What's wrong with the proof? Assuming NP=co-NP, an instance F of TQBF can be solved by a polynomial NDTM this way: Non-...
Ajay's user avatar
  • 147
-4 votes
1 answer
1k views

Alternative Turing Machine Proofs

I am asking this question again. I am aware of, and have read the other similar "alternative proof TM" questions, but unfortunately, they do help me. I am looking for a TM Halting Problem proof that ...
johne's user avatar
  • 227