Problem Detail: I looked at here for getting an intuition about F-algebra, but I am still left with some questions. Suppose I have a group signature as $Sigma= (* : X times X rightarrow X, thicksim: X rightarrow X , e Read More …
Category: Uncategorized
[Solved]: Why does the solution of an NP problem have to be polynomial size?
Problem Detail: I’ve read in “Introduction to Algorithms” (CLRS) that formal language $L$ is NP-language if and only if there is a polynomial verification algorithm $A(x, y)$ and a constant $c$ such that $$L={xin{0,1}mid exists y text{ with } |y| leq Read More …
[Solved]: Smallest string length to contain all types of beads
Problem Detail: I read this question somewhere, and could not come up with an efficient answer. A string of some length has beads fixed on it at some given arbitrary distances from each other. There are $k$ different types of beads Read More …
[Solved]: Fundamental Boolean Functions
Problem Detail: I can define any boolean function (I think) using and and not, or using or and not (plus a constant 0 or 1). And I can define or in terms of xor. And then there are nor and nand. Read More …
[Solved]: Is there an always-halting, limited model of computation accepting $R$ but not $RE$?
Problem Detail: So, I know that the halting problem is undecidable for Turing machines. The trick is that TMs can decide recursive languages, and can accept Recursively Enumerable (RE) languages. I’m wondering, is there a more limited model of computation which Read More …
[Solved]: Reducing from Hamiltonian Cycle problem to the Graph Wheel problem cannot be proved vice versa
Problem Detail: I saw a proof by Saeed Amiri, We will add one extra vertex v to the graph G and we make new graph G′, such that v is connected to the all other vertices of G. G has a Read More …
[Solved]: What techniques can I use to hand-write a parser for an ambiguous grammar?
Problem Detail: I’m writing a compiler, and I’ve built a recursive-descent parser to handle the syntax analysis. I’d like to enhance the type system to support functions as a valid variable type, but I’m building a statically typed language, and my Read More …
[Solved]: Recursive language subtracted from recursively enumerable language
Problem Detail: This is a homework problem but I am awfully confused. The problem reads as follows: If $L_1$ is recursively enumerable but not recursive, and $L_2$ is recursive, then which of the following is the strongest true statement about the Read More …
[Solved]: Why is b-tree search O(log n)?
Problem Detail: B-tree is a data structure, which looks like this: If I want to look for some specific value in this structure, I need to go through several elements in root to find the right child-node. The I need to Read More …
[Solved]: Deleting useless (dead) states from a finite automaton
Problem Detail: A useless state in a finite automaton is one from which no path leads to a final state, hence no (piece of a string) is recognized out of this state. Theoretically, the algorithm to determine the useful states is Read More …