Problem Detail: Say I have an undirected finite sparse graph, and need to be able to run the following queries efficiently: $IsConnected(N_1, N_2)$ – returns $T$ if there is a path between $N_1$ and $N_2$, otherwise $F$ $ConnectedNodes(N)$ – returns the Read More …
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[Solved]: Would creating a complete computer simulation of the human brain prove the Church-Turing thesis?
Problem Detail: According to Wikipedia, the Church-Turing thesis “states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing machine.” If we made a complete Read More …
[Solved]: How does this non-deterministic algorithm to find if a Hamiltonian path exists work?
Problem Detail: I have read of an algorithm that a non-deterministic Turing machine $N$ can run to determine whether a given graph $G$ has a Hamiltonian path from the start node $s$ to a certain node $n$: Write a list of Read More …
[Solved]: Time complexity of Dynamic Array via repeated doubling
Problem Detail: When we implement dynamic array via repeated doubling (if the current array is full) we simply create a new array that is double the current array size and copy the previous elements and then add the new one? Correct? Read More …
[Solved]: Constrainted Optimization Problem in Matrix Entropy
Problem Detail: I have a constrainted optimization problem in the (Shannon) matrix entropy $mathtt{(sum(entr(eig(A))))}$. The matrix $A$ can be written as the sum of rank 1 matrices of the form $[v_i,v_i^T]$ where $v_i$ is a given normalized vector. The coefficients of Read More …
[Solved]: Optimal algorithm for finding all ngrams from a pre-defined set in a text
Problem Detail: I’m thinking about the optimal algorithm for the following problem: Input data: a text, say it’s an article about 5-50 pages. a set of ngrams (ngram strings, n>2), of arbitrary length, could be more than 20k n-grams. The algorithm Read More …
[Solved]: Shortest path with odd weight
Problem Detail: Let G be a directed graph with non-negative weights. We call a path between two vertices an “odd path” if its weight is odd. We are looking for an algorithm for finding the weight of the shortest odd path Read More …
[Solved]: Consistency and completeness imply soundness?
Problem Detail: I understand that soundness implies consistency. Also, I understand that consistency alone does not imply soundness. But shouldn’t consistency + completeness imply soundness? Scott Aaronson in his blog-post hints otherwise. What am I exactly missing? Update: By completeness I Read More …
[Solved]: Can a Big-Oh time complexity contain more than one variable?
Problem Detail: Let us say for instance I am doing string processing that requires some analysis of two strings. I have no given information about what their lengths might end up being, so they come from two distinct families. Would it Read More …
[Solved]: Need a practical solution for creating pattern database(5-5-5) for 15-Puzzle
Problem Detail: I have asked this exact question on StackOverflow. I did not get the answer that I was looking for. Please read this question fully before answering. Thank You. For static pattern database(5-5-5), see this(page 290 and 283) OR there Read More …
