Problem Detail: In reading some blogs about computational complexity (for example here)I assimilated the notion that deciding if two groups are isomorphic is easier than testing two graphs for isomorphism. For example, on the stated page it says that graph isomorphism Read More …
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[Solved]: definition of formula validity
Problem Detail: I read in some sources that valid formulas are tautologies (valid under every evaluation). In the others, I read that these are formulas that have conclusions true when premises are true. Are these just equivalent definitions because ⊨ P Read More …
[Solved]: How do computers create ‘randomness’?
Problem Detail: I have just used a function ‘rand()’ in my algorithm. In fact, it was arc4random() that I used. However, it got me thinking, how is randomness created in a computer system? Can anything ever truly be random when it Read More …
[Solved]: Why are lambda-abstractions the only terms that are values in the untyped lambda calculus?
Problem Detail: I am confused about the following claim: “The only values in the untyped lambda calculus are lambda-abstractions”. Why are the other terms not values? What does it mean for a lambda-abstraction to be a value? The first thing that Read More …
[Solved]: Find the minimum range
Problem Detail: Given a list of numbers as L, how do you find the minimum value m such that L can be made into a strictly ascending list by adding or subtracting values from [0,m] from each element of L except Read More …
[Solved]: Does location transparency imply access transparency?
Problem Detail: In distributed systems theory, I have found the definition that a distributed system requires, among others, location and access transparency. I was wondering if location transparency does not already include access transparency. Wikipedia defines the two as follows: Access Read More …
[Solved]: Can we do better than $O(nlog n)$ building a balanced binary tree?
Problem Detail: I’m (foolishly it turns out) confident that the answer to this question is no. So why am I asking? Because Dr. Aleksandar Prokopec at EPFL in his parallel programming course introduces a data-structure for which he asserts various properties. Read More …
[Solved]: Algorithm to check the distance between integers
Problem Detail: I have the next problem, and I was wondering whether it exists a way to solve it without having to iterate around all the array in the worst case. I have a sorted array of pairwise distinct integers, say Read More …
[Solved]: The Hindley-Milner type system plus polymorphic recursion is undecidable or semidecidable?
Problem Detail: I have often read that Hindley-Milner extended to allow polymorphic recursion is undecidable. However is the term used what is actually meant? Or do people actually mean semidecidable when they mention that? I ask this before I’ve recently found Read More …
[Solved]: Heap-like data structure allowing peek at largest & smallest
Problem Detail: For the purpose of implementing an optimization algorithm (finding the minimum of a multivariate function) I want to create a data structure that supports the following operations: load from array Peek at maximum element (but don’t destroy it) Peek Read More …
