Problem Detail: I’m trying to find the answers of two questions about the Universal Turing machine. How can the Universal Turing machine simulate a Turing machine if the one that is being simulated has a bigger number of states? How can Read More …
Author: ignougroup
[Solved]: Is there a basic proof that there exists some edit distance between two strings?
Problem Detail: Title says it all pretty much. I do realize that often edit distance is defined as the minimum number of operations needed to transform one string to another, but I want something to point to that’s even more general 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 …
[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 …
