Problem Detail: I read a claim that there are formulas for which any equivalent CNF has exponential length. Can you show me an example for such a boolean formula? I have been trying to build it myself and failed. Asked By Read More …
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[Solved]: Choosing taps for Linear Feedback Shift Register
Problem Detail: I am confused about how taps are chosen for Linear Feedback Shift Registers. I have a diagram which shows a LFSR with connection polynomial $C(X) = X^5 + X^2 + 1$. The five stages are labelled: $R4, R3, R2, Read More …
[Solved]: Is the height of the tree the number of edges or number of nodes?
Problem Detail: I’m so confused by some of the theorems online about tree heights. Does tree height mean the number of edges or nodes? if nodes, does it include the node it is counting from? Can the height of a tree Read More …
[Solved]: Is this a divide-and-conquer algorithm?
Problem Detail: I’d like to start by stating this isn’t homework! I’m studying for a job interview and would appreciate a second opinion. (Well, I guess it is homework, but not for school!). I’ve written an algorithm (see pseudocode below) to Read More …
[Solved]: Proof of Ramsey’s theorem: the number of cliques or anti cliques in a graph
Problem Detail: Ramsey’s theorem states that every graph with $n$ nodes contains either a clique or an independent set with at least $frac{1}{2}log_2 n$ nodes. I tried to look it up at a few places (including Sipser) but I could not Read More …
[Solved]: Pumping lemma for CFG doubt
Problem Detail: I was looking at the pumping lemma for CFG. I came across the first problem $a^nb^nc^n$ and understood the answer. Then I thought of the problem $a^nb^n$. I know that this is context free and thought of applying it. Read More …
[Solved]: Hoare triple for assignment P{x/E} x:=E {P}
Problem Detail: I am trying to understand Hoare logic presented at Wikipedia, Hoare logic at Wikipedia Apparently, if I understand correctly, a Hoare triple $${P}~ C ~{Q}$$ means if P just before C, then Q holds immediately after C, as long Read More …
[Solved]: What does the R superscript notation mean in regular/formal languages?
Problem Detail: What does the capital R superscript notation mean in regular languages? I am working on a homework assignment and don’t recall my professor mentioning what the what the R superscript means. For example in this syntax: $L = {ww^Rmid Read More …
[Solved]: 3/2 – Approximation probabilistic algorithm for MAX-3-COLOR
Problem Detail: I have a textbook question here regarding Max-3-Coloring and need some assistance with it. I have searched for any type of information regarding it but haven’t found anything substantial. Here is the question: In MAX-3-COLOR you are given a Read More …
[Solved]: Understanding an example of coin toss expectation maximization
Problem Detail: I’ve been trying to get my head around Expectation maximization algorithms, and I thought I’d start simple. I found this 3-coin example here: http://cs.dartmouth.edu/~cs104/CS104_11.04.22.pdf I understand the calculation of all of the probabilities but I don’t understand how the Read More …
