Problem Detail: Suppose I have an application with two threads, which both use the same resource. Normally, a synchronized block keeps these threads from messing with the resource in a way the user doesn’t expect. I understand why you do this, Read More …
Category: Uncategorized
[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 …
[Solved]: Number of Independent Sets in a tree
Problem Detail: (I’ve been stuck on this homework assignment for far too long) I need to find the number of independent sets in a tree. For example, say the set of nodes in a tree is {A, B, C, D, E}. Read More …
[Solved]: Showing that the entropy of i.i.d. random variables is the sum of entropies
Problem Detail: The shannon entropy of a random variable $Y$ (with possible outcomes $Sigma={sigma_{1},…,sigma_{k}}$) is given by $H(Y)=-sumlimits_{i=1}^{k}P(Y=sigma_{i});log(P(Y=sigma_{i}))$. For a second random variable $X=X_{1}X_{2}…X_{n}$, where all $X_{i}$’s are independent and equally distributed (each $X_{i}$ is a copy of the same random Read More …
[Solved]: Running time of CDCL compared to DPLL
Problem Detail: What’s the complexity of Conflict-Driven Clause Learning SAT solvers, compared to DPLL solvers? Was it proven that CDCL is faster in general? Are there instances of SAT that are hard for CDCL but easy for DPLL? Asked By : asd Read More …
[Solved]: A greedy approximation algorithm for max k-cut
Problem Detail: The max k-cut problem is: Given an undirected graph G= (V;E) with nonnegative edge costs, and an integer k, find a partition of V into sets $S_1,cdots,S_k$ so that the total cost of edges running between these sets is Read More …
[Solved]: $mathbf{NC}$ is closed under logspace reductions
Problem Detail: I am trying to solve the question 6.12 in Arora-Barak (Computational Complexity: A modern approach). The question asks you to show that the $mathsf{PATH}$ problem (decide whether a graph $G$ has a path from a given node $s$ to Read More …
[Solved]: Double hashing – probe count probabilities
Problem Detail: From TAoCP, Vol. 3 by Knuth we know that expected (mean) probe counts for hash tables with open adressing and double hashing collision-resolution are: $1 over 1 – alpha$ – for unsuccessful search ${1 over alpha} ln({1 over 1 Read More …
