Category: Uncategorized

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 …

Problem Detail: From this statement As there is no surjection from $mathbb{N}$ onto $mathcal{P}(mathbb{N})$, thus there must exist an undecidable language. I would like to understand why similar reasoning does not work with a finite set $B$ which also has no Read More …

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: I would like to know how Boyer-Moore text searching algorithm with Galil’s rule works,. I tried to search for but I couldn’t understand the information I found, for example this Wikipedia page. And why with this rule we go Read More …

Problem Detail: I’ve encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve. Recently I was asked this question and did not even know what algorithmic technique to use to answer it! There are Read More …

Problem Detail: I’m trying to understand/show that DNF VALID is coNP-hard. I have given an algorithm for the complement of DNF VALID and shown that this is in NP (since the complement of a language in NP is in coNP), but Read More …