Author: ignougroup

Problem Detail: Reachability is defined as follows: a digraph $G = (V, E)$ and two vertices $v,w in V$. Is there a directed path from $v$ to $w$ in $G$? Is it possible to write a polynomial time algorithm for it? Read More …

Problem Detail: From the book Computer organization and design by Patterson&Hennessy: Parity is a function in which the output depends on the number of 1s in in the input. For an even parity function, the output is 1 if the input Read More …

Problem Detail: Let $$L_ = {langle Mrangle mid M text{ is a Turing Machine that accepts the string 1100}}, .$$ To proof that the language $L$ is undecidable I should reduce something to $L$, right? I tried with the classic $A Read More …

Problem Detail: In Algorithmic Randomness and Complexity from Downey and Hirschfeldt, it is stated on page 129 that $qquad displaystyle sum_{K(sigma)downarrow} 2^{-K(sigma)} leq 1$, where $K(sigma)downarrow$ means that $K$ halts on $sigma$, $sigma$ being a binary string. $K$ denotes the prefix-free Read More …

Problem Detail: I am looking at an example Turing machine in my textbook, Automata and Computability by Dexter C. Kozen, and I’m confused as to how they determine the number of states this particular machine has. Here is the example: “Here Read More …

Problem Detail: While trying to improve the performance of my collision detection class, I found that ~80% of the time spent at the gpu, it spent on if/else conditions just trying to figure out the bounds for the buckets it should Read More …

Problem Detail: I am wanting to try and prove that the English language is not regular. The alphabet is the set of all words in the English dictionary. Looking at sentences, I was able to use this pattern of sentences { Read More …

Problem Detail: I am aware of using Bellman-Ford on a graph $G=(V,E)$ with no negative cycles to find the single-source single-destination shortest paths from source $s$ to target $t$ (both in $V$) using at most $k$ edges. Assuming we have no Read More …

Problem Detail: I’m reading The Art of Multiprocessor Programming and am currently trying to understand Chapter 4 — The Foundations of Shared Memory. In section 4.2 it is shown how to build a multi-reader, single-writer (MRSW) safe Boolean register from a Read More …

Problem Detail: I have two sets B which is recursively enumerable and is not recursive, and A which is recursive. Is $A-B$ recursive and / or recursively enumerable? What about $B-A$? $B-A$ is obviously recursively enumerable (to generate its elements, I Read More …