Problem Detail: Many people say that TAOCP is not supposed to be read as a book (actually a volume of books), but if I decide to go that way, which math/computer science books/topics do I need to study to help me Read More …
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Do not understand why log n = O(n^c) (for any c>0)
Problem Detail: Can anyone help me understand this equation? $log (n) = O(n^c)$ (for any $c>0$) Does it mean that $O(log (n)) < O(n^c)$ (for any $c>0$)? Added: Please also prove that $log (n) = O(n^c)$ is true. Asked By : Xin Read More …
Kleene positive closure – help in proofing this claim
Problem Detail: I just started a course called ‘Automata and Formal Languages’. I’m having difficulty in proofingdisproofing this equality. $ (L_{1} circ L_{2})^{+} = L_{1}^{+} circ L_{2}^{+} $ Where: $ L_{1} $, $L_{2}$ are Languages. $circ$ is the concatenation operation between Read More …
Relation of Space and Time in Complexity?
Problem Detail: I’m looking for some clarification on some concepts/facts I came across while studying for a class. I was reading the following wikipedia article. The below specific section and statement intrigued me when looking it over. http://en.wikipedia.org/wiki/Computational_complexity_theory#Important_complexity_classes “It turns out Read More …
Show that the Kleene star of any unary language is regular
Problem Detail: An exercise asks me to show that the Kleene star of any unary language $L$ is regular. $E$ is the alphabet, $E = { 1 }$ Here’s my reasoning : $L$ is regular $implies$ $L^*$ is regular (closure property) Read More …
Are there any PSPACE problems that don’t exist in NP-Hard?
Problem Detail: The question is in the title, I suppose. I am studying complexity classes, and I understand that NP-Hard is the set of problems that are at least as hard as the hardest problems in NP. Therefore, it will naturally Read More …
Converting NFA to DFA
Problem Detail: I’ve converted an NFA to a DFA. But even after checking over it a few times, it still doesn’t feel right. I’m sure this is trivial, but I’d like someone to give me an idea where I went totally Read More …
Are there improvements on Dana Angluin’s algorithm for learning regular sets
Problem Detail: In her 1987 seminal paper Dana Angluin presents a polynomial time algorithm for learning a DFA from membership queries and theory queries (counterexamples to a proposed DFA). She shows that if you are trying to learn a minimal DFA Read More …
Dual-pivot Quicksort reference implementation?
Problem Detail: Has some sort of canonical – or reference – implementation of Dual-pivot Quicksort been posted anywhere? I would like to include that algorithm in a comparison among sorting algorithms for a specialized need that I have, but the Java Read More …
Round robin tournament scheduling using divide and conquer
Problem Detail: I want to scheduling $n$ teams using divide and conquer method for $n in mathbb{N}$.My approach is that if $n$ is even divide it to to group $frac{n}{2}$ and $frac{n}{2}$ but if $n$ is odd, add auxiliary team and Read More …
