Problem Detail: You are given n integers $a_1, ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$’s form a non-decreasing sequence. Define the Read More …
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Show that Vertex-Cover is NP-complete, using Stable-Set
Problem Detail: My task is to give proof, the Vertex-Cover problem is NP-complete, assuming it’s already shown that the Stable-Set problem is NP-complete, too. My approach: i know, Stable-Set is NP-complete, and all Problems that are NP-complete can be reduced to Read More …
Reducing directed hamiltonian cycle to graph coloring
Problem Detail: The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time? Asked By : Johan Sannemo Read More …
A pumping lemma for deterministic context-free languages?
Problem Detail: The pumping lemma for regular languages can be used to prove that certain languages are not regular, and the pumping lemma for context-free languages (along with Ogden’s lemma) can be used to prove that certain languages are not context-free. Read More …
Recursive equation for complexity: T(n) = log(n) * T(log(n)) + n
Problem Detail: For analyzing the running time of an algorithm , I’m stuck with this recursive equation : $$ T(n) = log(n) cdot T(log n) + n $$ Obviously this can’t be handled with the use of the Master Theorem, so Read More …
Decidable non-context-sensitive languages
Problem Detail: It is arguable that most languages created to describe everyday problems are context-sensitives. In the other hand, it is possible and not hard to find some languages that are not recursive or even not recursively-enumerable. Between these two types Read More …
Find an MST in a graph with edge weights from {1,2}
Problem Detail: I’ve been asked the following question: Given a connected undirected graph $G=(V,E)$ and a weight function $w: E to {1,2}$, suggest an efficient algorithm that finds an MST of the graph. After a few clarifications, the algorithm should run Read More …
Matrix Chain Multiplication Greedy Approach
Problem Detail: In the question Matrix Chain Multiplication you are given a chain of Matrices and is required to find the optimal way to multiply the matrices together. Normally this is solved using Dynamic Programming but I have found a greedy Read More …
What are the possible sets of word lengths in a regular language?
Problem Detail: Given a language $L$, define the length set of $L$ as the set of lengths of words in $L$: $$mathrm{LS}(L) = {|u| mid u in L }$$ Which sets of integers can be the length set of a regular Read More …
Can a Turing Machine decide only non-regular languages?
Problem Detail: I have an assignment where i need to create a Turing machine that decides an infinite language $Lsubset {0,1}^*$ for which all $L’subseteq L$, if $|L’|=infty$, then $L’$ is not a regular language. I think this is not possible Read More …
