Author: ignougroup

Problem Detail: It is known that there are problems in P that, provably, are not solvable in less than $O(N^k)$, for some $k$. Now consider some infinite set $K subseteq mathbb{R}^+_0$ such as K is unbounded from above (you can think Read More …

Problem Detail: Is there a proof or reference that $left{text{MAX},text{MIN}right}text{-True-2-XOR-SAT}$ is $NP$-hard, or that it (the decision version) is in $P$? Let: $$Phileft(mathbf xright)={hugewedge}_{i}^{n}C_i, forall_{C_i} left.C_i=(p oplus q)right|_{left(pin mathbf x veeneg pinmathbf xright),left(qin mathbf x veeneg qinmathbf xright)} $$ The $text{2-XOR-SAT}$ Read More …

Problem Detail: Let’s say we have a directed graph $G = (V, E)$ for which $(v, w) in E$ and/or $(w,v) in E$ holds true for all $v, w in V$. My feeling is that this graph most definitely is Hamiltonian, Read More …

Problem Detail: I learned from this post that ${sf DTIME}^{text{EXP}}(n^k) neq text{EXP}$ for a fixed $k$ for otherwise the Time Hierarchy Theorem would fail in that relativized world. However, is it possible to prove that no oracles exist in which the Read More …

Problem Detail: I am working on my cs project about AI & Turing machines, so i know that Artifical Intelligence is meant to implement different algorithms into the machine {the computer} to solve a problem or a set of problems together Read More …

Problem Detail: Let $T$ be a depth-first search tree of a connected undirected graph $G$ and $h$ be the height of $T$. How do you show that $G$ has no more than $h times |V|$ edges where $|V|$ is the number Read More …

Problem Detail: This is a follow up to my earlier questions on coinduction and bisimulation. A relation $R subseteq S times S$ on the states of an LTS is a bisimulation iff $forall (p,q)in R,$ $$ begin{array}{l} text{ if } p Read More …

Problem Detail: Can a Boolean circuit by itself be considered an algorithm (a single step algorithm if you like)? For instance say you have a simple tree circuit with two AND gates as the input gates feeding a single OR gate Read More …

Problem Detail: Let’s consider distributed version of algorithm for finding MIS of any graph $A$. For details, MIS – Maximimal Independent Set. Slow version of distributed algorithm for MIS, page 2 – Distributed algorithms. Maximal Independent Set In worst case, time Read More …

Problem Detail: Here is my implementation of mergeSort. I need n extra space for the helper array. But what about recursive calls? I call sort log n times. mergeRoutine is a tail call, and it doesn’t add to the call stack. Read More …