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 …
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[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 …
[Solved]: Does Ford-Fulkerson always produce the left-most min-cut
Problem Detail: When using Ford-Fulkerson to find max-flow between s and t, the exact choice of flow-graph depends on which paths are found. However, if you then use the left-over residual graph to produce a min-cut (by flood-filling outward from s Read More …
[Solved]: If $L$ is a regular language, how to prove $L_1 = { uv mid u in L, |v| =2 }$ is also regular?
Problem Detail: If $L$ is a regular language, prove that the language $L_1 = { uv mid u in L, |v| =2 }$ is also regular. My idea: $L$ can be represented as a DFA and then you could add Read More …
[Solved]: Clique decision problem restricted to a subgraph
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 …
[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 …
