Problem Detail: I thought that any FOT is a subset of FOL, but that does not seem to be the case, because FOL is complete (every formula is either valid or invalid), while some FOT (like linear integer arithmetic) is not Read More …
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[Solved]: Why does this pumping lemma application “prove” that 0*1* is not regular?
Problem Detail: Here is a proof that $0^*1^*$ is not regular, even though it is regular. I’m having a hard time figuring out what is wrong with the proof. Assume $0^*1^*$ is regular. Let $p$ be the pumping length as defined Read More …
[Solved]: Concrete understanding of difference between PP and BPP definitions
Problem Detail: I am confused about how PP and BPP are defined. Let us assume $chi$ is the characteristic function for a language $mathcal{L}$. M be the probabilistic Turing Machine. Are the following definitions correct: $BPP ={mathcal{L} :Pr[chi(x) ne M(x)] geq Read More …
[Solved]: How can I fill bookcases with shelves of books using the least number of bookcases?
Problem Detail: Sorry for layman’s term question, my background in computer science is weak. What I have is a list of shelves with books of varying height. Each shelf stores a value that describes how many shelves (of that height) can 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 …
[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]: 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]: 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]: 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]: 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 …
