Category: Uncategorized

Problem Detail: Has it been proven that Dijkstra’s algorithm is optimal for asymptotic worst case of single-source shortest path on directed graphs? (Assume no preprocessing) I became curious when Wikipedia mentioned it as the ‘best known’ rather than the ‘best possible’. Read More …

Problem Detail: I’m looking for a proof to the claim stated in the title: if $Lin NPcap Co-NP$ is $NP$-Hard, then $NP=Co-NP$. I read the proof from my professor’s recitation, but couldn’t understand it, and I was hoping to find more Read More …

Problem Detail: Let $Sigma = {0,1}$. For every word $w in Sigma^*$, let $|w|_0$ and $|w|_1$ denote the count of 0’s and 1’s, respectively, in $w$. Let $L$ be the language $$L = { w in Sigma^* mid |w|_0 gt |w|_1 Read More …

Problem Detail: I just started reading “Parsing Techniques, A Practical Guide”, Second Edition, by Dick Grune and Ceriel J.H. Jacobs. On page 12, the authors start describing a set of rules that can be used to generate the set of all Read More …

Problem Detail: Let there be 2 sets $X$ and $Y$, both are countable (assume the bijection from $mathbb{N}$ to the respective sets is computable) and infinite. Let $S$ be the set of all possible functions (NOT necessarily computable, i dont care Read More …

Problem Detail: The set difference operator (e.g., EXCEPT in some SQL variants) is one of the many fundamental operators of relational algebra. However, there are some databases that do not support the set difference operator directly, but which support LEFT JOIN Read More …

Problem Detail: As far I know, in general case there is no Turing machine which could get any theorem on its input and produce its proof on its output. Why is it so? Asked By : peterh Answered By : Jake We have Read More …

Problem Detail: I am currently attending the concurrent programming course in my university and we recently started talking about the concept of a monitor. While I understand the necessity of mutual exclusion, I do not understand why I would use a Read More …

Problem Detail: I’d really like your help with the proving or refuting the following claim: $BPP(0.90,0.95)=BPP$. In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in Read More …

Problem Detail: I am looking for an algorithm with time complexity in $mathcal O(|V|)$ that determines whether a given graph $G=(V,E)$ is a caterpillar tree. A caterpillar tree is a tree that has a path to which all nodes are connected Read More …