Problem Detail: The problem whether two pushdown automata recognize the same language is undecidable. The problem whether a pushdown automata recognizes the empty language is decidable, hence it is also decidable whether it recognizes a given finite language. It is undecidable Read More …
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[Solved]: Complexity of 3SAT variants
Problem Detail: This question is motivated by my answer to another question in which I stated the fact that both Betweeness and Non-Betweeness problems are $NP$-complete. In the former problem there is a total order such that the betweeness constraint of Read More …
[Solved]: What’s the difference between Adaptive Control and a Kalman Filter?
Problem Detail: From my basic understanding of Adaptive Control, I understand that it uses the error and the velocity of the error to approximate the error in the solution space of a problem, thus allowing for guaranteed convergence under certain conditions Read More …
[Solved]: Is this a divide-and-conquer algorithm?
Problem Detail: I’d like to start by stating this isn’t homework! I’m studying for a job interview and would appreciate a second opinion. (Well, I guess it is homework, but not for school!). I’ve written an algorithm (see pseudocode below) to Read More …
[Solved]: Is the height of the tree the number of edges or number of nodes?
Problem Detail: I’m so confused by some of the theorems online about tree heights. Does tree height mean the number of edges or nodes? if nodes, does it include the node it is counting from? Can the height of a tree Read More …
[Solved]: Choosing taps for Linear Feedback Shift Register
Problem Detail: I am confused about how taps are chosen for Linear Feedback Shift Registers. I have a diagram which shows a LFSR with connection polynomial $C(X) = X^5 + X^2 + 1$. The five stages are labelled: $R4, R3, R2, Read More …
[Solved]: Formulas for which any equivalent CNF formula has exponential length
Problem Detail: I read a claim that there are formulas for which any equivalent CNF has exponential length. Can you show me an example for such a boolean formula? I have been trying to build it myself and failed. Asked By Read More …
[Solved]: Search for minimum in an array of $k$ monotonic subarrays
Problem Detail: Let $A$ be an array of totally ordered elements. A subarray $A[i..j]$ is decreasing if $A[k]geq A[k+1]$ for all $i leq k < j$. It is increasing if $A[k]leq A[k+1]$ for all $i leq k < j$. It is Read More …
[Solved]: Number of 1 child nodes in a binary tree
Problem Detail: Does anybody know how would I approach calculating the maximum number of 1 child nodes (nodes that have exactly 1 child) in a binary tree with n nodes. Please don’t give me the actual answer as this is one Read More …
[Solved]: A heuristic for finding a maximum disjoint set
Problem Detail: Background I need to find a largest set of non-overlapping axis-parallel squares, out of a given collection of candidate squares. This problem is NP-complete. Many papers suggest approximation algorithms (see Maximum Disjoint Set in Wikipedia), but I need an Read More …
