Problem Detail: It is arguable that most languages created to describe everyday problems are context-sensitives. In the other hand, it is possible and not hard to find some languages that are not recursive or even not recursively-enumerable. Between these two types Read More …
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Recursive equation for complexity: T(n) = log(n) * T(log(n)) + n
Problem Detail: For analyzing the running time of an algorithm , I’m stuck with this recursive equation : $$ T(n) = log(n) cdot T(log n) + n $$ Obviously this can’t be handled with the use of the Master Theorem, so Read More …
A pumping lemma for deterministic context-free languages?
Problem Detail: The pumping lemma for regular languages can be used to prove that certain languages are not regular, and the pumping lemma for context-free languages (along with Ogden’s lemma) can be used to prove that certain languages are not context-free. Read More …
Reducing directed hamiltonian cycle to graph coloring
Problem Detail: The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time? Asked By : Johan Sannemo Read More …
Can a Turing Machine decide only non-regular languages?
Problem Detail: I have an assignment where i need to create a Turing machine that decides an infinite language $Lsubset {0,1}^*$ for which all $L’subseteq L$, if $|L’|=infty$, then $L’$ is not a regular language. I think this is not possible Read More …
B-Tree and how it is used in practice
Problem Detail: I understand what a B-Tree is (I already implemented a B-Tree in Java with insert and delete methods that preserve the invariant). However I do not understand exactly how it is used for example for file systems or databases. Read More …
What are the mathematical prerequisites for adaptive machine learning algorithms?
Problem Detail: I am a PhD student in Computer Science who switched his PhD a little bit towards ML algorithms combined with something else… I am an expert in that something else, say image processing, but not an expert in Machine Read More …
What would we call this datastructure?
Problem Detail: Suppose we have a datastructure that is a list containing elements that are either a leaf or another layer of the datastructure (recursively defined). What would we call this? It isn’t a tree, since it has variable number of Read More …
No compression algorithm can compress all input messages?
Problem Detail: I just started reading a book called Introduction to Data Compression, by Guy E. Blelloch. On page one, he states: The truth is that if any one message is shortened by an algorithm, then some other message needs to Read More …
Is this formal grammar context-free (CFG) but not context-sensitive (CSG)?
Problem Detail: I have the following formal grammar: $$G= ({S,A,B},{a,b},R,S)$$ $$R={S rightarrow A |B, A rightarrow varepsilon | aA |bA, B rightarrow varepsilon |Bb | b}$$ Now, we see, the production rules $A rightarrow varepsilon$ and $B rightarrow varepsilon$ implies that Read More …
