Problem Detail: We are given an array $A[1..n]$ of integers, and an array of 3-tuples known as queries. The query tuples $(i,j,v)$ denote additions of an integer $v$ to the subarray of $A[i..j]$. I’m interested in the query time of $A[k]$ Read More …
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[Solved]: What was going on before PAC learning
Problem Detail: I am investigating PAC learning (computational learning theory) as a beginner with no previous knowledge of machine learning / AI. I am investigating the model mainly from a historical point of view. For this, the most important things are Read More …
[Solved]: Unification — most specific unifier
Problem Detail: In unification, given a set of equations, a standard problem is to compute a most general unifier (mgu). I am interested in a somewhat reversed problem. Imagine having a set of equations that do not have an mgu, like Read More …
[Solved]: Complexity of the decision version of determining a min-cut
Problem Detail: I was wondering what the complexity of the following problem is: Given: A flow network $N$ with a source $s$, sink $t$ and a number $k$. Question: Is there an $s$-$t$ cut of capacity at most $k$? Obviously, the Read More …
[Solved]: Small-step semantics: for-loops
Problem Detail: I’m trying to construct the small-step semantic rules involving the for-loops, but I can’t find anything about it in the literature (only about while-loops). I was wondering if anyone could help me out with this? This is a first Read More …
[Solved]: If P != NP, then 3-SAT is not in P
Problem Detail: I hope I’m in the right section: I know that if P = NP, then 3-SAT can be solved in P (Cook), but is the opposite valid, too? If P != NP, then 3-SAT is not in P? Thanks! Read More …
[Solved]: Is the set cover problem NP-complete when the cardinality of the collection of sets is equal to the cardinality of the universe?
Problem Detail: In the set cover (SC) problem we are given a universe $U$ (a set) of $n$ elements and a collection $S$ of $m$ sets whose union equals the universe. The set cover problem is to identify the smallest sub-collection Read More …
[Solved]: Algorithm for length of longest common subsequence
Problem Detail: The case of multiple strings. A slight modification of the dynamic programming algorithm for two strings is used as a subroutine. Here is the pseudo code: # The modified dynamic programming algorithm for longest common subsequence. # Inputs: x, Read More …
[Solved]: Finding Minimum Weight Subgraph Spanning Tree
Problem Detail: Suppose we have a graph $G = (V, E, w:ein E to x in {0,1})$. That is, a set of vertices, a set of edges and a weight function that assigns edges weights of 0 or 1. Suppose we Read More …
[Solved]: If $L_1L_2$ is regular language then $L_2L_1$ is regular to?
Problem Detail: We have two languages: $L_1,L_2$. We know that $L_1L_2$ is regular language, so my question is if $L_2L_1$ is regular to? I try to find a way to prove it… I can’t assume of course that $L_1,L_2$ are regular… Read More …
