Problem Detail: Suppose I am given an array of $n$ fixed width integers (i.e. they fit in a register of width $w$), $a_1, a_2, dots a_n$. I want to compute the sum $S = a_1 + ldots + a_n$ on a Read More …
Category: Uncategorized
[Solved]: Notions of efficient computation
Problem Detail: A polynomial-time Turing machine algorithm is considered efficient if its run-time, in the worst-case, is bounded by a polynomial function in the input size. I’m aware of the strong Church-Turing thesis: Any reasonable model of computation can be efficiently Read More …
[Solved]: Does ln n ∈ Θ(log2 n)?
Problem Detail: Is that statement false or true? I believe it’s false because ln(n) = log base e of n. So therefore, log base 2 of n can be a minimum because in 2^x = n, x will always be less Read More …
[Solved]: does godel’s incompleteness theorem shed any light on dynamic vs typed languages?
Problem Detail: I’m clojure user myself. I’m trying really hard to learn haskell and to better understand the type system. However, I feel that trying to ‘type’ everything is quite restrictive when the problem or the data is less defined. I Read More …
[Solved]: Turing machine working only with 1’s and blanks – how to encode input?
Problem Detail: Let’s say we have a Turing machine which head can only write 1 or blank to the tape (although it can read all symbols from any input alphabet correctly). Can we operate with it on any input? My approach Read More …
[Solved]: Pumping lemma for Context-Free Languages
Problem Detail: I have a question about a specific pumping lemma problem for Context-Free Languages. Suppose we have the following Language: $L = {a^{i}b^{j}c^{k}d^{l} mid 0 < i < k wedge j > l > 0 }$ Here is my attemp Read More …
[Solved]: Why not relax only edges in Q in Dijkstra’s algorithm?
Problem Detail: Can someone tell me why almost in every book/website/paper authors use the following: foreach vertex v in Adjacent(u) relax(u,v) when relaxing the edges, instead of: foreach vertex v in Adjacent(u) if (v is in Q) relax(u,v) This is extremely Read More …
[Solved]: Proving a Language is Irregular using Myhill-Nerode
Problem Detail: I’m trying to prove that the language: begin{equation*} L = { w in { 0, 1 }^* : w text{ contains more 0’s than 1’s} } end{equation*} is irregular using the Myhill-Nerode theorem. I’ve been through all the basic Read More …
[Solved]: How exactly do you calculate the hidden layer gradients in the backpropagation algorithm?
Problem Detail: I have been going through the description of the backpropagation algorithm found here. and I am having a bit of trouble getting my head around some of the linear algebra. Say I have a final output layer $L$ consisting Read More …
[Solved]: Why aren’t we researching more towards compile time guarantees?
Problem Detail: I love all that is compile time and I love the idea that once you compile a program a lot of guarantees are made about it’s execution. Generally speaking a static type system (Haskell, C++, …) seems to give Read More …
