Problem Detail: You have two friends, call them A and B. They each are given two wine bottles: one bottle holds k_1 litres and the other k_2 litres. Both A and B can perform these operations: – completely fill a wine Read More …
Author: ignougroup
[Solved]: Proving Regularity of Languages that are 1/k of an already known regular language
Problem Detail: There is this question in Kozen, that states if a language is regular then the first half would also be regular. Also I found a material on the internet that extends the thinking saying a language that is two-thirds Read More …
[Solved]: Why does many to one reduction imply Turing reducibility?
Problem Detail: So, $ Aleqslant_mB $ (many to one reduction) means that language $A$ can be reduced to language $B$ if there exists a Turing-calculable function $f$ so $ f(A) subseteq B$ and $ f(overline{A}) subseteq overline{B} $. $ Aleqslant_TB $ Read More …
[Solved]: Origins of the term “distributed hash table”
Problem Detail: I am currently researching for my diploma thesis in computer science with a topic in the area of distributed hash tables. Naturally, I came to the question were the term distributed hash table came from. (I know it is Read More …
[Solved]: A puzzle related to nested loops
Problem Detail: For a given input $N$, how many times does the enclosed statement executes? for $i$ in $1ldots N$ loop $quad$for $j$ in $1ldots i$ loop $quad$$quad$for $k$ in $ildots j$ loop $quad$$quad$$quad$$sum = sum + i$ ; $quad$$quad$end loop; Read More …
[Solved]: What is the decidable language in $P/poly$ but not in $P$?
Problem Detail: Except for the undecidable unaries I have no idea if there is anything in the gap between $P/poly$ and $P$ Asked By : user6818 Answered By : Yuval Filmus Take a language $L$ which is not in $mathsf{E} = bigcup_{c=1}^infty mathsf{TIME}(2^{cn})$. Read More …
[Solved]: Count number of special onto functions
Problem Detail: We define an onto function from $[n] times [n]$ to $[n-2] cup {0}$ as follows, where $[n] = {1,2,3,ldots ,n}$, $$f : [n] times [n] rightarrow [n-2] cup {0}.$$ 1) $f(x,x) = 0$. 2) $f(x,y) = f(y,x) > 0$, Read More …
[Solved]: Complexity of transposing matrices represented as list of row or column vectors
Problem Detail: Given [[1,4,7],[2,5,8],[3,6,9]] which is a list of the column vectors of matrix |1, 2, 3| |4, 5, 6| |7, 8, 9| is $ Omega(n^2) $ a lower bound for transposing? Assume the matrix is not always square. I have Read More …
[Solved]: showing that the pair of Finite Automata are equivalent
Problem Detail: Here I am trying to show that the pair of Finite Automata are equivalent. I have tried something but I am not sure if I am in the right direction. This is what I have. These are pairs of Read More …
[Solved]: If the decision problem can be solved in poly time, show the optimization problem also can
Problem Detail: Here is a problem I am trying to solve: The bin packing decision problem is defined as follows: given an unlimited number of bins, each of capacity equal to $1$, and $n$ objects with sizes $s_1$, $s_2$, $dots$, $s_n$ Read More …
