Author: ignougroup

Problem Detail: According to Wikipedia, the Church-Turing thesis “states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing machine.” If we made a complete Read More …

Problem Detail: In Richard Gabriel’s famous essay The Rise of Worse is Better, he contrasts caricatured versions of the MIT/Stanford (Lisp) and New Jersey (C/Unix) design philosophies along the axes of simplicity, correctness, consistency, and completeness. He gives the example of Read More …

Problem Detail: Let’s consider a memory segment (whose size can grow or shrink, like a file, when needed) on which you can perform two basic memory allocation operations involving fixed size blocks: allocation of one block freeing a previously allocated block Read More …

Problem Detail: I was reading the article about the SHA1 hashing function (I know it is not secure anymore) and I’ve found a pseudocode implementation on Wikipedia. I can see that there are a lot of mathematical operations, and what I Read More …

Problem Detail: This is probably a stupid question, but I just don’t understand. In another question they came up with Schaefer’s dichotomy theorem. To me it looks like it proves that every CSP problem is either in P or in NP-complete, Read More …

Problem Detail: We are going over the pumping lemma in class and we recently went over the following example: Let $$ L = { w mid w text{ has a different number of 0s and 1s} } $$ Consider $$ s Read More …

Problem Detail: I just learned PDAs in class today, but am having problems understanding the syntax of the transition function. Could someone please explain to me the meaning of this syntax: $delta(q, lambda, S) = {(q, aaB), (q, bbA)}$ This is Read More …

Problem Detail: The problem of deciding whether an input is a palindrome or not has been proved to require $Omega(log n)$ space on a Turing machine. However, even storing the input takes space $n$ so doesn’t that mean that all Turing machines Read More …

Problem Detail: Let’s say I have a graph $|G|$ with $|E|=O(V^2)$ edges. I want to run BFS on $G$ which has a running time of $O(V+E)$. It feels natural to write that the running time on this graph would be $O(O(V^2)+V)$ Read More …

Problem Detail: $log(n)$ is not polynomial; is a problem solvable in $mathcal{O}(log n)$ time in P? $ntimes log(n)$ is also not polynomial; is a problem solvable in $mathcal{O}(ntimes log n)$ time in P? If not, what complexity classes contain those problems? Read More …