Problem Detail: I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you Read More …
Author: ignougroup
[Solved]: Operations on OBDD: negation through Shannon’s expansion
Problem Detail: I have a problem with the application of the Shannon expansion for to obtain the negation of a formula boolean, than will need for implement the negation operator on OBDD (Order Binary Decision Diagram) that is, show that: $qquad Read More …
[Solved]: Choosing an element from a set satisfying a predicate uniformly at random in $O(1)$ space
Problem Detail: We are given a set of objects, say integers, $S$. In addition, we are given a predicate $P$, for example $P(i): Leftrightarrow i geq 0$. We don’t know in advance how many elements of $S$ satisfy the predicate $P$, Read More …
[Solved]: Standard constructive definitions of integers, rationals, and reals?
Problem Detail: Natural numbers are defined inductively as (using Coq syntax as an example) Inductive nat: Set := | O: nat | S: nat -> nat. Is there a standard way to define integers (and maybe other sets like rationals and Read More …
[Solved]: Why is determining the size of a maximum independent set or a clique in P?
Problem Detail: I read that determining the size of the maximum independent set (and also a clique of maximum size) is in P. The versions that find the actual solution are known to be NP-hard. With respect to finding clique size, Read More …
[Solved]: Which computational model is used to analyse the runtime of matrix multiplication algorithms?
Problem Detail: Although I have already learned something about the asymptotic runtimes of matrix multiplication algorithms (Strassen’s algorithm and similar things), I have never found any explicit and satisfactory reference to a model of computation, which is used to measure this Read More …
[Solved]: Does this mean $P = NP$
Problem Detail: I am not a formally trained guy on Complexity theory, but due to interest I am learning it. Based on different feedbacks, I have started my journey with Micheal Sipser’s “Theory of Computation” (2013 edition). My question is based Read More …
[Solved]: Converting a non-planar graph to planar
Problem Detail: Suppose that we have a non-planar graph $G$ which is undirected and connected. Our aim is to remove a set of edges and/or a set of vertices and convert make $G$ planar while keeping the connectedness. Besides connectedness, $G$ Read More …
[Solved]: Longest simple walk in a complete graph
Problem Detail: A simple walk is a path that does not contain the same edge twice. A simple walk can contain circuits and can be a circuit itself. It just shouldn’t have the same edge twice. A simple undirected graph is Read More …
[Solved]: A lambda calculus evaluation involving Church numerals
Problem Detail: I understand that a Church numeral $c_n$ looks like $lambda s. lambda z. s$ (… n times …) $s;z$. This means nothing more than “the function $s$ applied $n$ times to the function $z$”. A possible definition of the Read More …
