Problem Detail: Being a programmer I appreciate the errors given by a compiler for a programming language and come to rely on the compiler’s error as a safety net. In learning category theory I would like to have some tool that Read More …
Category: Uncategorized
[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]: Does stay put TM recognizes same languages as standard TM
Problem Detail: I am reading this text book and it says that stay put turing machine recognizes the same languages as regular turing machine by just adding transition functions (without adding any new states or symbols). I am trying to figure 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]: What does it mean for a random number generator’s sequence to be only 1-dimensionally equidistributed?
Problem Detail: Whilst reading up on Xorshift I came across the following (emphases added): The following xorshift+ generator, instead, has 128 bits of state, a maximal period of 2^128 − 1 and passes BigCrush: [snip code] This generator is one of Read More …
