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 …
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[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 …
[Solved]: How to decribe an action with STRIPS?
Problem Detail: The state space is decribed with 3 boolean variables $p,q$ and $r$ (so we have 8 states total). We have an action, let’s say $a$. Action $a$ can be executed when $p=text{False}$ and $q=text{True}$ and the result is $p=text{True}$, Read More …
[Solved]: Can we test whether two vertices are connected in time linear in the number of nodes?
Problem Detail: Consider the problem: Given an undirected graph and two of its vertices, is there a path between them? I often read that this problem can be solved in linear time in the number of vertices! I am not sure Read More …
[Solved]: Number of clique in random graphs
Problem Detail: There is a family of random graphs $G(n, p)$ with $n$ nodes (due to Gilbert). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of size $k$ in $G(n, Read More …
