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Problem Detail: Alternative Formulation I came up with an alternative formulation to the below problem. The alternative formulation is actually a special case of the problem bellow and uses bipartite graphs to describe the problem. However, I believe that the alternative Read More …
Problem Detail: For a language L we define: $qquad A(L) = { x in L mid text{ no proper prefix of x is in L} } $ Are regular / context free languages closed under this operation ? For regular languages Read More …
Problem Detail: Yesterday I was reading about Computability and they mention the Halting Problem. It got stuck in mind all day until I remember that some weeks ago, when learning Java, the IDE (Netbeans) show me a warning saying that my Read More …
Problem Detail: I have started to study non deterministic automata using the book of Hopcroft and Ullman. I’m stuck in a problem that I found very interesting: Give a non deterministic finite automaton accepting all the strings that have the same Read More …
Problem Detail: Given a complete binary tree with $n$ nodes. I’m trying to prove that a complete binary tree has exactly $lceil n/2 rceil$ leaves. I think I can do this by induction. For $h(t)=0$, the tree is empty. So there Read More …
Problem Detail: I asked my algorithms teacher today the very same question that is stated in the title, but he seemed a bit unsure, either on the question or on the concept, so I thought I’d try here too. Is there Read More …
Problem Detail: $newcommand{np}{mathsf{NP}}newcommand{cc}{textrm{Circuit-SAT}}$I am having difficulty understanding the $np$-hardness proof for $cc$ in CLRS. $cc = {langle C rangle : C text{ is a satisfiable combinatorial boolean circuit} }$ Lemma: The $cc$ problem is $mathsf{NP}$-hard. Can anyone provide an easy-to-understand proof? Read More …
Problem Detail: Consider directed graphs. We call a node $v$ superstar if and only if no other node can be reached from it, but all other nodes have an edge to $v$. Formally: $qquad displaystyle $v$ text{ superstar } :Longleftrightarrow mathrm{outdeg}(v) Read More …
Problem Detail: Consider 2 stations that share the same bus. Both stations are perfect synchronized each other and when they have packets to transmit, they are starting the transmission in the beginning of a same slot. Transmission is as follows: when Read More …
Problem Detail: I’m trying to solve 17-2(b) problem from Cormen(CLRS) using potential method. Problem from Cormen: 17-2 Making binary search dynamic Binary search of a sorted array takes logarithmic search time, but the time to insert a new element is linear Read More …
