Problem Detail: Given three numbers $m$, $n$ and $p$ in interleaved binary encoding1, it’s obviously possible to check in $O(1)$ space whether $m+n=p$. It’s less obvious2 that it isn’t possible to check in $O(1)$ space whether $mcdot n=p$. I wonder whether Read More …
Author: ignougroup
[Solved]: Finding all marked elements using Grover’s algorithm
Problem Detail: Grover’s algorithm uses an oracle function $f(x) to {0,1}$ to find the location of a single marked element from an unordered database of $2^n$ elements with high probability. As part of an assignment I am supposed to design a Read More …
[Solved]: Solving a complicated recurrence relation
Problem Detail: How to solve the recurrence relation below? $$T(n) = begin{cases} 2T(sqrt{n}) + log n/loglog n & text{if } n > 4 1 & text{if } n leq 4. end{cases}$$ Preferably by the master theorem; otherwise by any method. I Read More …
[Solved]: Reference request: proof that if $L in DCFL$, then $L Sigma^* in DCFL$
Problem Detail: So, it’s fairly easy to prove that if $L in DCFL$, then $L Sigma^* in DCFL$. Basically, you take the DPDA accepting $L$. You remove all transitions on final states, and then for each $a in Sigma$ and each Read More …
[Solved]: Decidability of the language that accepts a universal turing machine
Problem Detail: Is the language $L_{universal} = { left langle M right rangle | M textrm{is a universal turing machine} }$ decidable? I’m guessing it is decidable according to the definition of a UTM, that a UTM must be able to Read More …
[Solved]: Implications of Rice’s theorem
Problem Detail: Every time I think I get what Rice’s theorem means, I find a counterexample to confuse myself. Maybe someone can tell me where I’m thinking wrong. Lets take some non-trivial property of the set of computable functions, for example Read More …
[Solved]: Can a perceptron forget?
Problem Detail: I would like to build an online web-based machine learning system, where users can continuously add classified samples, and have the model updated online. I would like to use a perceptron or a similar online-learning algorithm. But, users may Read More …
[Solved]: Algorithm: Dimension increase in 1D representation of Square Matrix
Problem Detail: Consider the matrix with dimension $m times m$: $$ M = begin{array}{cc} 1 & 1 & 1 0 & 1 & 1 1 & 0 & 1 end{array} $$ Its 1-D representation: $$ M^* = begin{array}{cc} 1 & 1 Read More …
[Solved]: Algorithm to match timestamped events from two sources
Problem Detail: does a good known algorithm exists for this problem? On input I have two series of timestamps “when the event was observed”. Theoretically the recorded timestamps should be very well aligned. Visualized ideal situation on two time lines “s” Read More …
[Solved]: Understanding Intel’s algorithm for reducing a polynomial modulo an irreducible polynomial
Problem Detail: I’m reading this Intel white paper on carry-less multiplication. It describes multiplication of polynomials in $text{GF}(2^n)$. On a high level, this is performed in two steps: (1) multiplication of polynomials over $text{GF}(2)$, and (2) reducing the result modulo an Read More …
