Problem Detail: As per the title I was wondering if it’s possible for a language $L subseteq Sigma^{*}$ to have $Sigma^{*}$ as its syntactic monoid and if so could one give an example of such a language? I first thought that Read More …
Author: ignougroup
[Solved]: Which theoretical parallel model is closest to CUDA?
Problem Detail: Which theoretical parallel model is closest to CUDA/OpenCL programming model? For example, it fits at some degree to the generic Parallel Random Access Machine (PRAM) model. However, that is too generic, since it makes abstraction of various memory access Read More …
[Solved]: How do I find the shortest representation for a subset of a powerset?
Problem Detail: I’m looking for an efficient algorithm for the following problem or a proof of NP-hardness. Let $Sigma$ be a set and $Asubseteqmathcal{P}(Sigma)$ a set of subsets of $Sigma$. Find a sequence $win Sigma^*$ of least length such that for Read More …
[Solved]: Represent string as concatenations
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 …
[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 …
