Problem Detail: I was looking at the construction proof showing the equivalence of NFA and DFA from Sipser’s text. It started by taking number of states of DFA as $mathcal{P}(Q)$, where $mathcal{P}(Q)$ is the set of subsets of $Q$. My doubt Read More …
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[Solved]: Difference between diameter of a graph vs longest path of the graph
Problem Detail: I am curious what is the difference between diameter of a graph vs longest path of a graph. I just read diameter of a graph can be solved using Floyd warshall in O(V^3) while longest path can be calculated Read More …
[Solved]: Can we represent all computer programs as graphs?
Problem Detail: I was thinking the other day, and it occurred to me that computer programs all seem to be representable as a graph (an abstract syntax tree for example), or, once common expressions are combined, an abstract syntax graph. It Read More …
[Solved]: Given a tree, find a vertex which maximizes the minimum distance to any leaf
Problem Detail: If I am given a graph which forms a tree, I am interested in finding a vertex which maximizes the minimum distance to any leaf. I am sure this problem has been studied before. Does anybody know the name Read More …
[Solved]: Running Time of Modular Exponentiation
Problem Detail: I am trying to understand why the modular exponentiation algorithm has a running time of about $log(n)$ where $n$ is the exponent. Here is the algorithm: function modular_pow(base, exponent, modulus) result := 1 while exponent > 0 if (exponent Read More …
[Solved]: Can we make a non-regular language regular via concatentation?
Problem Detail: My question is basically given three languages A, B and L, where L is A and B concatenated together and B is proven to be non regular, is it possible to find an A that makes L regular? Asked Read More …
[Solved]: Can’t understand why the DP Subset Sum algorithm is not polynomial
Problem Detail: I can not understand why the dynamic programming algorithm for the Subset Sum, is not polynomial. Even though the sum to find ‘T’ is greater than the total sum of the ‘n’ elements of the set , the number Read More …
[Solved]: What are the practical uses of ontologies?
Problem Detail: I have read many papers and books about ontologies and I am trying to figure out that how they are used in a real project? For example how the ontology for a soccer player robot can be defined and Read More …
[Solved]: Using a step-counting function in a Turing Machine construction
Problem Detail: I have an question relating to the elementary foundations of Turing Machine theory. I would like to have a clarification of the status of a function $phi$ (a mapping between TM indexes) I shall introduce in the formal question Read More …
[Solved]: How much complexity difference can there be between finding a solution to a Sudoku puzzle and PROVING that the solution is the unique solution?
Problem Detail: So usually Sudoku is $9 times 9$, but this question extends to $n^2 times n^2$ puzzles with $n > 3$ as well. There are many polynomial time deduction rules that can make progress in finding a solution to a Read More …
