Author: ignougroup

Problem Detail: If I have a system of N polynomial equations with N unknowns in GF(2): What are some good methods to solve them? What’s the highest value of N that can be reasonable solved? Now, my root interest isn’t GF, Read More …

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 …

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 …

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 …

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 …

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 …

Problem Detail: $L={<!M,x!>, mid M’s text{ transition function can only move right and } Mtext{ halts on } x }$. I need to show that $L$ is recursive/decidable. I thought of checking the encoding of $M$ first and determine whether its Read More …

Problem Detail: I am studying some lecture notes on the complexity of algorithms. The notes give a proof that NP is not a proper subset of coNP. However, they still assert that NP is a subset of coNP (which I agree Read More …