Category: Uncategorized

Problem Detail: A source provides a stream of items $x_1, x_2,dots$ . At each step $n$ we want to save a random sample $S_n subseteq { (x_i, i)|1 le i le n}$ of size $k$, i.e. $S_n$ should be a uniformly Read More …

Problem Detail: Are there any “natural” examples of decidable problems that are definitively known not to be in NP? The decidable languages I know of that are not contained in NP are usually derived from the time hierarchy theorem, which produces Read More …

Problem Detail: I consider Point Location Problem in Polygon in repetitive mode in the case of simple polygon. In computational geometry,Point Location Problem in Polygon problem asks whether a given point in the plane lies inside, outside, or on the boundary Read More …

Problem Detail: I am looking for implementation of the set data type. That is, we have to maintain a dynamic subset $S$ (of size $n$) from the universe $U = {0, 1, 2, 3, dots , u – 1}$ of size Read More …

Problem Detail: According to Wikipedia: Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained representation of that string. What is the analogous informal rigorous Read More …

Problem Detail: I saw from this post on stackoverflow that there are some relatively fast algorithms for sieving an interval of numbers to see if there is a prime in that interval. However, does this mean that the overall decision problem Read More …

Problem Detail: Suppose that we have a black-box $f$ which we can query and reset. When we reset $f$, the state $f_S$ of $f$ is set to an element chosen uniformly at random from the set $${0, 1, …, n – Read More …

Problem Detail: I’m reading Homer and Selman’s “Computability and Complexity” book. In some Corollary 5.3 it says: For all ε‎ > 0, DTIME(O(n)) = DTIME( (1+ε‎‎) n). Now I’m confused with this corollary and Rosenberg’s result (p87 in the same book): Read More …

Problem Detail: I’m curious. I’ve been working on this datatype in OCaml: type ‘a exptree = | Epsilon | Delta of ‘a exptree * ‘a exptree | Omicron of ‘a | Iota of ‘a exptree exptree Which can be manipulated using Read More …