Problem Detail: Given a weighted, undirected graph $G = (V,E)$, how can I compute the average weight of edges? It seems an easy problem (divide the total weight to the number of edges!) but I couldn’t manage to find the sum Read More …
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[Solved]: Ordering elements so that some elements don’t come between others
Problem Detail: Given an integer $n$ and set of triplets of distinct integers $$S subseteq {(i, j, k) mid 1le i,j,k le n, i neq j, j neq k, i neq k},$$ find an algorithm which either finds a permutation $pi$ Read More …
[Solved]: Relation between logspace-uniform circuits and P-uniform circuits
Problem Detail: In the book “Computational complexity” of Barak and Arora, on page 112, they state that: Theorem 6.15: A language has logspace-uniform circuits of polynomial size iff it is in P. The proof of this one is left as an Read More …
[Solved]: Algorithms which are both deterministic and non-deterministic
Problem Detail: I’m just starting my second year in computer science and one of my classes briefly touched upon deterministic vs. non-deterministic algorithms. This got me thinking – is there any use for algorithms which return deterministic output for certain inputs, Read More …
[Solved]: Are neural networks dynamical systems?
Problem Detail: Dynamical systems are those whose evolution can be described by a rule, evolves with time and is deterministic. In this context can I say that Neural networks have a rule of evolution which is the activation function $f(text{sum of Read More …
[Solved]: How to find left-hand side of tape on a Turing Machine?
Problem Detail: I am pretty new to Turing Machines and am trying to figure something out. So let’s say I have a tape with input 0 0 1 0 0 1 The language is twice as many 0’s than 1’s. So Read More …
[Solved]: example for weakly fair v.s. strongly fair scheduling in concurrency
Problem Detail: I am having difficult time understanding the difference between weakly fair and strongly fair schedulers. Can someone provide an example and explain how they are different? for reference, here are the definitions I have of each: weakly fair: A Read More …
[Solved]: Proving non-regularity of $u u^R v$?
Problem Detail: This particular language: $$L = { u u^R v ,:, u, v in {0, 1}^+}$$ is giving me a lot of trouble. I highly suspect that its non-regular, considering that ${ u u^R : u in {0, 1}^+}$ is Read More …
[Solved]: purpose of supercomputers
Problem Detail: Last fall I went on a tour of the Blue Waters supercomputer at the University of Illinois. I asked whether anyone ever used the entire computer. I was told that it was always working on multiple projects. That made Read More …
[Solved]: Terminology for a graph with ports on its nodes
Problem Detail: A Graph is a well-defined concept in mathematics, computer science and engineering disciplines that depend on them. However, oftentimes a practical implementation of a (directed) graph in a certain domain or application requires that edges don’t merely connect vertices, Read More …
