Problem Detail: I’m trying to prove that $exists L_1, L_2 : L_1$ and $L_2$ are context-free languages $land;L_1 cap L_2 = L_3$ is an undecidable language. I know that context-free languages are not closed under intersection. This means that I can Read More …
Author: ignougroup
[Solved]: Given two total Turing machines, is it undecidable problem to detect whether they give the same output on all inputs?
Problem Detail: See title. And by all inputs I mean providing the functions with the same input and checking whether they give the same output for each case. EDIT If it can be reduced to Halting problem, then how? EDIT 2 Read More …
[Solved]: Does “standard” Dijkstra’s algorithm work with bi-directional edges and zero cost edges?
Problem Detail: I have been reading about Dijkstra’s algorithm and I think I understand it. I followed the algorithm in pseudo-code from Wikipedia, and now I wonder: If my graph is bi-directional and I add each edge to my graph twice Read More …
[Solved]: Right moving turing machine
Problem Detail: I am interested in simulating any turing machine with a turing machine that is allowed only to move right. I guess that it should be pretty standard material and likely it is trivial (or known to be false). Does Read More …
[Solved]: $O(n^{k-1}$) algorithm for K-clique problem
Problem Detail: Clique problem is a well known $NP$-complete problem where the size of the required clique is part of the input. However, k-clique problem has a trivial polynomial time algorithm ($O(n^k)$ when $k$ is constant). I’m interested in the best Read More …
[Solved]: prove no DPDA accepts language of even-lengthed palindromes
Problem Detail: How do you prove that the language of even-lengthed palindromes, i.e., $L=left{ ww^R mid win leftlbrace 0,1 right}^* right}$, can not be accepted by a determinsitc Push-Down-Automaton? Is there any general way to prove that a context-free language can Read More …
[Solved]: prove language is Context-free and not regular
Problem Detail: I have to prove that $left { a, b right }^{ast} – left { a^ib^i | igeq 0 right }$ is a context-free language and it’s not regular. So far I’ve got that this language is not regular because Read More …
[Solved]: Reducing from a Turing machine that recognizes is regular to the halting problem
Problem Detail: I’m trying to understand reduction, this is from my textbook and is not a homework problem or even any exercise, just trying to understand an example they present. This is the reduction they give: PROOF We let R be Read More …
[Solved]: Load balancing. Why not use priority queues?
Problem Detail: I have recently learned about various randomized algorithms for load balancing. The model is always that there are $m$ balls and $n$ bins and the balls arrive one at a time. The task is to minimize the maximum load Read More …
[Solved]: Undirected graph with 12 edges and 6 vertices
Problem Detail: For school we have to make an assignment, and part of the assignment is this question: Describe an unidrected graph that has 12 edges and at least 6 vertices. 6 of the vertices have to have degree exactly 3, Read More …
