Problem Detail: Is there any “natural” language which is undecidable? by “natural” I mean a language defined directly by properties of strings, and not via machines and their equivalent. In other words, if the language looks like $$ L = { Read More …
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[Solved]: Number of binary trees with given height
Problem Detail: I was wondering how many binary trees we have with height of $h$ with $n$ nodes(another question is how many binary trees we have with height $ lfloor{lg (n)}rfloor$). Edit: I forgot to add the number of nodes. Asked Read More …
[Solved]: Efficient way to calculate sum in sliding window?
Problem Detail: Assume you have a grid as below: The square is the sliding window. I want to slide this window over all the possible position such that the window is contained in the grid (i.e the edges of the window Read More …
[Solved]: Is a 2 address machine more likely to follow a RISC or CISC design?
Problem Detail: The Problem: If I have a 3 address machine, is my machine more likely to follow RISC or CISC design? 2 addresses? 1 address? 0 address. To solve this problem I first looked up the different terms. RISC is Read More …
[Solved]: Is 0-1 integer linear programming NP-hard when $c^T$ is the all-ones vector?
Problem Detail: Karp’s 21 NP-complete problems show that 0-1 integer linear programming is NP-hard. That is, an integer linear program with binary variables. If we set the $c^T$ vector of the objective $text {maximize } c^Tx$ to all one (unweighted, i.e., Read More …
[Solved]: Why are regular expressions defined with union, concatenation and star operations?
Problem Detail: A regular expresssion is defined recursively as $a$ for some $a in Sigma$ is a regular expression, $varepsilon$ is a regular expression, $emptyset$ is a regular expression, $(R_1 cup R_2)$ where $R_1$ and $R_2$ are regular expressions is a Read More …
[Solved]: number of edges in a graph
Problem Detail: I got a problem related to graph theory – Consider an undirected graph ܩ where self-loops are not allowed. The vertex set of G is {(i,j):1<=i,j <=12}. There is an edge between (a, b) and (c, d) if |a-c|<=1 Read More …
[Solved]: Are there any problems that are easy to compute but hard to verify?
Problem Detail: Assuming P $neq$ NP, NP-complete problems are “hard to solve, but have answers that are easy to check.” Does it make any sense to consider the opposite, that is, problems for which it’s easy to compute a correct answer, Read More …
[Solved]: Equivalence of Turing Machines
Problem Detail: Consider the following two arguments “For every non deterministic TM M1 there exists an equivalent deterministic machine M2 recognizing the same language.“ “Equivalence of two Turing Machines is undecidable” These two arguments seem a bit contradicting to me. What Read More …
[Solved]: What is the use of finding minimum number of straight lines to cover a set of points?
Problem Detail: There is that popular problem [1] [2] in the computer science that is finding minimum number of straight lines that covers a given set of points in 2D. Even though I have scanned many papers, none of them has Read More …
