Problem Detail: I know that the clique problem is NP-complete. However, what if we change the problem a little bit? For example, Given a graph $G(V,E)$, an integer $k$ and a subset $S$ of $m$ vertices, we are given a decision Read More …
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[Solved]: Algorithm – Wine Bottle Filling
Problem Detail: You have two friends, call them A and B. They each are given two wine bottles: one bottle holds k_1 litres and the other k_2 litres. Both A and B can perform these operations: – completely fill a wine Read More …
[Solved]: Proving Regularity of Languages that are 1/k of an already known regular language
Problem Detail: There is this question in Kozen, that states if a language is regular then the first half would also be regular. Also I found a material on the internet that extends the thinking saying a language that is two-thirds Read More …
[Solved]: Why does many to one reduction imply Turing reducibility?
Problem Detail: So, $ Aleqslant_mB $ (many to one reduction) means that language $A$ can be reduced to language $B$ if there exists a Turing-calculable function $f$ so $ f(A) subseteq B$ and $ f(overline{A}) subseteq overline{B} $. $ Aleqslant_TB $ Read More …
[Solved]: Origins of the term “distributed hash table”
Problem Detail: I am currently researching for my diploma thesis in computer science with a topic in the area of distributed hash tables. Naturally, I came to the question were the term distributed hash table came from. (I know it is Read More …
[Solved]: Testing Polygon for Monotonicity
Problem Detail: It’s well known that Monotone polygon plays a crucial role in Polygon triangulation. Definiton: monotone polygon – a polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ Read More …
[Solved]: Counting trees (order matters)
Problem Detail: As a follow up to this question (the number of rooted binary trees of size n), how many possible binary trees can you have if the nodes are now labeled, so that abc is different than bac cab etc Read More …
[Solved]: $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular
Problem Detail: Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side. I need to Show that $L$ is regular. I’d relly like some help, I tried to think of any way to prove Read More …
[Solved]: Can finding a witness be NP-hard even if we already know there is one?
Problem Detail: The common examples of NP-hard problems (clique, 3-SAT, vertex cover, etc.) are of the type where we don’t know whether the answer is “yes” or “no” beforehand. Suppose that we have a problem in which the we know the Read More …
[Solved]: Proving a specific language is regular
Problem Detail: In my computability class we were given a practice final to go over and I’m really struggling with one of the questions on it. Prove the following statement: If $L_1$ is a regular language, then so is $L_2 = Read More …
