Problem Detail: Can someone help me understand the steps in this argument? There is a decision problem that is in $mathsf{cotext{-}NP}$ (under standard Karp reductions) and is $mathsf{NP}$-hard with respect to Cook reductions. Does this imply that if it is in Read More …
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[Solved]: Wiring Length Minimization
Problem Detail: My Problem is like this: I have a physical layout represented as a graph. The Nodes represents hooks/ducts where a wire can anchor and Edges are the possible connection between 2 nodes from where wire can go. There are Read More …
[Solved]: Enumerating all n-tuples over a finite domain
Problem Detail: I would like to create an algorithm which takes in an integer n and returns an array whose entries give all n-tuples of nonnegative integers each of which is at most n, so like A[n][0] = [0,0,0,…,0], A[n][1] = Read More …
[Solved]: Is there a complexity viewpoint of Galois’ theorem?
Problem Detail: Galois’s theorem effectively says that one cannot express the roots of a polynomial of degree >= 5 using rational functions of coefficients and radicals – can’t this be read to be saying that given a polynomial there is Read More …
[Solved]: Why we use context-free grammar for parsing?
Problem Detail: Why we use context-free grammar for parsing? Why not regular expression and not context-sensitive grammar? Asked By : Himanshu Saini Answered By : David Richerby Because regular expressions are too weak and context-sensitive languages are too difficult to parse. More specifically, Read More …
[Solved]: Is the image of a total, non-decreasing function decidable?
Problem Detail: This is an exercise I’ve been struggling with for a while: Let $g : mathbb{N} to mathbb{N}$ be a total, non-decreasing function, i.e. $forall x > y. g(x) geq g(y)$. Is the image $I_g$ of $g$ a recursive set? Read More …
[Solved]: Non-trivial runs of Prim’s algorithm
Problem Detail: What does it mean when we say that a run of Prim’s algorithm is trivial? What are example graphs for either case, that is with and without trivial runs? Asked By : fudu Answered By : Raphael Prim’s algorithm greedily chooses Read More …
[Solved]: What are appropriate isomorphisms between formal languages?
Problem Detail: A formal language $L$ over an alphabet $Sigma$ is a subset of $Sigma^*$, that is, a set of words over that alphabet. Two formal languages $L$ and $L’$ are equal, if the corresponding sets are extensionally equal as subsets Read More …
[Solved]: Direct NP-Complete proofs
Problem Detail: I’m just starting to learn about NP-completeness. While I understand that reducibility plays a key role in this, I’m astonished how few problems I’ve been able to find who’s proof that they are NP-Complete is not based on reduction Read More …
[Solved]: Algorithm to shrink a DFA by introducing nondeterminism?
Problem Detail: This is somewhat related to another question I asked, but I feel it’s different enough to warrant its own question. I’m doing research where I’m trying to find the structure of complements of a certain class of finite languages. Read More …
