Problem Detail: If $S_1,S_2$ are set of strings, then $S_1S_2 = {s_1s_2|s_1in S_1, s_2in S_2}$. $S^0={epsilon}$, $epsilon$ is the empty string. $S^n = S^{n-1}S$. Two related problems about represent string as concatenation of other strings. Given a finite set $S$ of Read More …
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[Solved]: Some slight confusion with the UNTIL operator in CTL (e.g. a U b)
Problem Detail: I’ve sketched a very small transition system in paint that I’ll use as an example. I want to see if $A(aUb)$ holds for this transition system. From my understanding, this CTL formula is asking if ALL paths satisfy $aUb$. Read More …
[Solved]: What is the “Chairman Tree”?
Problem Detail: My competitive programming coach told me of a balanced binary tree used by a lot of Chinese competitors that has all the functions of any other balanced binary tree and is fully persistent and runs queries and updates in Read More …
[Solved]: Turing Machines: Arbitrary alphabet equivalence with binary alphabet
Problem Detail: Think of an $n$-ary alphabet as ${0, 1, …, n-1, n}$. For example, a binary alphabet is ${0, 1}$. Do Turing Machines with binary alphabets decide the same set of languages as Turing Machines with $3$+ symbol alphabets? I Read More …
[Solved]: Pseudo-random sequence prediction
Problem Detail: Disclaimer: I am a biologist, so sorry for (perhaps) basic question phrased in such crude terms. I am not sure if I should ask this question here or on DS/SC, but CS is the largest of three, so Read More …
[Solved]: Is a language with only a stack of fixed-size integers Turing-complete?
Problem Detail: I encountered the brainfuck programming language which I know is turing complete. However I then decided to create a high level language that gets compiled to brainfuck code. There is only one data type in it (integer, since that’s Read More …
[Solved]: Running time of selection sort
Problem Detail: I wrote pseudocode for Selection Sort, but I’m not sure what is the running time of my algorithm, can you help me with that? My Pseudocode: Selection Sort(int a[], int n) Input: array of length $n$ Output: sorted array 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 …
