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- Approximating the dominating set on a certain kind of DAG
Your problem is a special case of set cover: The elements are the vertices and the sets are those formed as [v in V such that u=v or (u,v) in E] for elements u of V The size of those sets is bounded above by one plus your graph's maximum out-degree
- complexity theory - Showing Maximum Independent Set is $NP-hard . . .
Also, Clique and Independent Set are really the same problem — you get one from the other by complementing the graph Finally, let me stress that Independent Set is NP-complete, but it is not known to be in coNP or to be coNP-hard; indeed, it is conjectured not to be in coNP and not to be coNP-hard (otherwise NP=coNP)
- Is the set of all strings over $\\Sigma$ countably infinite or not?
Let $\Sigma$ be an alphabet Is the set of all strings over $\Sigma$ (i e $\Sigma^*$) countably infinite or uncountably infinite?
- graphs - All possible paths passing thru a set of nodes - Computer . . .
Start at a node with a counter variable at 0 and a set tracking what nodes have been visited, and a set of paths Visit each connected node, in order For each visited node, increment the counter by 1 and add the visited node to the tracking set
- turing machines - Proving a set is semi-decidable - Computer Science . . .
Proving a set is semi-decidable Ask Question Asked 6 years, 7 months ago Modified 6 years, 7 months ago
- complexity theory - Reducing Dominant Set Problem to SAT - Computer . . .
And that is by finding a propositional formula $\phi_{G,k}$ that is only satisfiable if and only if there exists a dominating set with no more than k vertices, so basically reducing it to SAT-Problem
- recursively enumerable - Intuition behind coRE or RE languages . . .
It is intuitive to think of languages that are in R For example, if we take a language EVEN, it is a set like so {2,4,6, } We say x is in the language if it is in the set How about languages that are coRE? For example, the Goldbach's conjecture that every natural number is either smaller than 3 or odd or the sum of two primes This is a
- complexity theory - Is the set of Turing machines that halt on . . .
In fact, GHP is very far from r e - it is $\Pi^0_2$-complete, meaning that in particular it is strictly more complicated (in the sense of Turing reducibility) than any r e set This includes the halting problem itself; in fact, GHP is Turing-equivalent to "the halting problem's halting problem "
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