Problem Detail: Let A and B be languages with A ⊆ B, and B is Turing-recognizable. Can A be not Turing-recognizable? If so, is there any example? Asked By : Wilhelm Answered By : Kaveh This is something that confuses many students. The Read More …
Blog
How to find max number with a single-tape turing machine?
Problem Detail: I’d appreciate hints for this problem I’m trying to design a Turing Machine which calculates $max {x_1, x_2,..,x_k }$. Assuming $1 = 1^1; 2=1^2; n=1^n$ and all numbers/strings are separated by a blank character $B$. Asked By : Iancovici Answered Read More …
Seating Chart Optimization
Problem Detail: I’m trying to find an algorithm to solve the seating chart problem. The goal is to place pepole at one (or multiple) tables such that the overall happiness is maximized. Each seat has neighbors. A person on a seat Read More …
Finding examples of languages that are “anti-palindromic”
Problem Detail: Let $Sigma = { 0, 1 }$. A language $L subseteq Sigma^* $ is said to have the “anti-palindrome” property if for every string $w$ that is a palindrome, $wnotin L$. In addition, for every string $u$ that is Read More …
What randomness really is
Problem Detail: I’m a Computer Science student and am currently enrolled in System Simulation & Modelling course. It involves dealing with everyday systems around us and simulating them in different scenarios by generating random numbers in different distributional curves, like IID, Read More …
Proving a grammar only generates words whose alternating digit sums are multiples of three
Problem Detail: This is homework and I’m looking for a push in the right direction. Proofs were never something I was properly taught, so now they’re kind of a weak point. Here’s the problem: The following grammar generates numbers in binary Read More …
Recurrence relation with sum
Problem Detail: This is a question about recurrence relation that contains sum inside the recursion.I am totally stuck. Can anyone help? The problem asks to solve the following recursion $T(n)=frac{1}{n} sum_{i=1}^{n-1}(T(i)+T(n-i))+cn$. The problem also warns that unwrapping is going to be Read More …
Computing the clustering coefficient
Problem Detail: I saw in this video that computing clustering coefficient of central node of a star graph using the following algorithm is $Theta(n^2)$ and for a clique it is $Theta(n^3)$. is that correct? def clustering_coefficient(G,v): neighbors = G[v].keys() if len(neighbors) Read More …
Does there exist a Turing complete typed lambda calculus?
Problem Detail: Do there exist any Turing complete typed lambda calculi? If so, what are a few examples? Asked By : Snowball Answered By : Gilles Yes, sure. Many typed lambda calculi accept only strongly normalizing terms, by design, so they cannot express Read More …
Closure of CFL against right-quotient with regular languages
Problem Detail: Let $A/B$ = ${ w mid wx in A$ for some $x in B }$. Show that if A is context free and B is regular, then $A/B$ is context free. My interpretation of this is is that Read More …