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1
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1answer
166 views

Polygonal Mersenne numbers [closed]

I posted the same question on Math SE since this one got put on hold. Link to Math SE question:Polygonal Mersenne numbers Polygonal numbers are of the form $\cfrac {n^2(s-2)-n(s-4)}{2}$, where $s$ ...
-1
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1answer
61 views

How to generate computational data in graph theory?

For a given number of nodes how many non-isomorphic graphs are available? Might be this is an open problem. For less number of vertices some computational statistics available. I want to get all ...
0
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0answers
55 views

Bits of precision matrix reconstruction

We have a real rank $r$ matrix $M\in\{0,1\}^{n\times n}$. Suppose we have diagonalized using $LMR=D$. I want to recover a real matrix $\widetilde{M}$ such that maximum absolute entry of ...
3
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2answers
178 views

efficiently checking that a field extension is Galois

Let $K \subset L$ be an algebraic extension of fields finitely presented over a prime field or over an algebraically closed field. Is there an efficient procedure to check that $L/K$ is Galois? To ...
0
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1answer
153 views

Refutation of $A \land \lnot\lnot\lnot A$ by resolution [closed]

$ A \land \lnot\lnot\lnot A $ this is a very simple example. Resolution is refutation complete. So it should be able to refute this formula. However, I don't see how would it do that without using ...
3
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0answers
68 views

Weak randomness relative to finite-state machines

Is there a nice example of a sequence that looks random to any predictor whose predictions use a finite-state machine? More precisely, consider a finite-state machine $M$ with input alphabet {0,1} ...
4
votes
5answers
296 views

procedure-based (as opposed to definition-based) concepts

Euler's work on divergent series was guided by computational procedures, rather than any definition of the "value" of such a series. E.g., he was happy to have half a dozen procedures that indicated ...
0
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3answers
386 views

System of quadratic equations with 18 unknown

So I want to solve for a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r which satisfy the following system of equations: ( I only need positive integer (or 0) solution) a g + c h + b i + g j + i ...
48
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14answers
3k views

Important open problems that have already been reduced to a finite but infeasible amount of computation

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer." Some questions ...
15
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3answers
1k views

What to do when your research runs into a computationally challenging problem?

Occasionally, but more frequently lately, I would like to perform some hard computations. As an example, yesterday the following question came up: What is the projective dimension of the edge ...
3
votes
1answer
460 views

Efficiently computing with pullbacks and pushouts

Often when computing in category theory, one has to show that some square is cartesian. Depending on the number of maps involved, and their arrangement, it's somewhat difficult to write down exactly ...