Category: Uncategorized

Problem Detail: Do “inductively” and “recursively” mean very similar? For example, if there is an algorithm that determines a n-dim vector by determine its first k+1 components based on its first k components having been determined, and is initialized with the Read More …

Problem Detail: Given normally distributed integers with a mean of 0 and a standard deviation $sigma$ around 1000, how do I compress those numbers (almost) perfectly? Given the entropy of the Gaussian distribution, it should be possible to store any value Read More …

Problem Detail: So based on the Chandy/Misra section in this Wikipedia article we’ve got 5 philosophers numbered P1-P5. Based on this quote: For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with Read More …

Problem Detail: Is the language $L = { a^ib^j mid i nmid j } $ context free ? If we fix $n in N$ then we know that the language $L = { a^ib^j mid forall 1 le k le n Read More …

Problem Detail: I am using a digital computer to write this message. Such a machine has a property which, if you think about it, is actually quite remarkable: It is one machine which, if programmed appropriately, can perform any possible computation. Read More …

Problem Detail: The algorithm that is used by gcc and llvm is that of Keith D. Cooper, Timothy J. Harvey, and Ken Kennedy (page 9). We start with the immediate dominators of each control-flow graph node B already calculated and stored Read More …

Problem Detail: I would like an example of a quine in pure lambda calculus. I was quite surprised that I couldn’t find one by googling. The quine page lists quines for many “real” languages, but not for lambda calculus. Of course, Read More …

Problem Detail: Wiki define Polynomial time as fallow: An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, i.e., $T(n) = O(n^k)$ Read More …

Problem Detail: In class our professor showed us 3 methods for proving non-regularity: Myhill–Nerode theorem Pumping Lemma for regular languages Proof of non-regularity, based on the Kolmogorov complexity Now the first two, Myhill-Nerode theorem and Pumping lemma, I understood well and Read More …

Problem Detail: Is there an efficient algorithm which computes the (possibly approximately) shortest $n$-edge path between two points $A$ and $B$ in a weighted complete graph? Dijkstra won’t work because it will just give the trivial answer of $Ato B$. I’d Read More …