Problem Detail: Does coNP-completeness imply NP-hardness? In particular, I have a problem that I have shown to be coNP-complete. Can I claim that it is NP-hard? I realize that I can claim coNP-hardness, but I am not sure if that terminology Read More …
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How to prove regular languages are closed under left quotient?
Problem Detail: $L$ is a regular language over the alphabet $Sigma = {a,b}$. The left quotient of $L$ regarding $w in Sigma^*$ is the language $$w^{-1} L := {v mid wv in L}$$ How can I prove that $w^{-1}L$ is regular? Read More …
How can I improve my Algorithm?
Problem Detail: This is a problem from Interview Street in Dynamic Programming section. https://www.interviewstreet.com/challenges/dashboard/#problem/4f2c2e3780aeb Billboards(20 points) ADZEN is a very popular advertising firm in your city. In every road you can see their advertising billboards. Recently they are facing a Read More …
The physical implementation of quantum annealing algorithm
Problem Detail: From that question about differences between Quantum annealing and simulated annealing, we found (in commets to answer) that physical implementation of quantum annealing is exists (D-Wave quantum computers). Can anyone explain that algorithm in terms of quantum gates and Read More …
How can P =? NP enhance integer factorization
Problem Detail: If ${sf P}$ does in fact equal ${sf NP}$, how would this enhance our algorithms to factor integers faster. In other words, what kind of insight would this fact give us in understanding integer factorization better? Asked By : Mike Read More …
Why do you have to worry about cache coherence if you are using shared memory?
Problem Detail: Wikipedia says that shared memory comes with lots of costs associated with cache coherence costs. But I thought the whole idea of shared memory is that all the CPUs access the same memory? So if one CPU changes that Read More …
What is the decision version of independent set?
Problem Detail: I always read that finding an independent set of size $k$ in a graph is $mathsf{NP}$-complete. However, this only requires looking for all combinations of $k$ vertices and this is a polynomial procedure of order $k$. I know that Read More …
Define a list using only the Hindley-Milner type system
Problem Detail: I’m working on a small lambda calculus compiler that has a working Hindley-Milner type inference system and now also supports recursive let’s (not in the linked code), which I understand should be enough to make it Turing complete. The Read More …
Algorithms with polynomial time complexity of higher order
Problem Detail: I was learning about algorithms with polynomial time complexity. I found the following algorithms interesting. Linear Search – with time complexity $O(n)$ Matrix Addition – with time complexity $O(n^2)$ Matrix Multiplication – with time complexity $O(n^3)$ Is there any Read More …
Subtracting lower-order term to prove subtitution method works
Problem Detail: Substation method fails to prove that $T(n)=Theta(n^2) $ for the recursion $T(n)=4T(n/2) + n^2$, since you end up with $T(n) < cn^2 leq cn^2 + n^2$. I don’t understand how to subtract off lower-order term to prove that substitution Read More …
