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 …
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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]: 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 …
[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]: 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]: Probabilty that quicksort partition creates an imbalanced partition
Problem Detail: I have come across this question: Let 0<α<.5 be some constant (independent of the input array length n). Recall the Partition subroutine employed by the QuickSort algorithm, as explained in lecture. What is the probability that, with a randomly Read More …
[Solved]: How to apply the pumping lemma to ${0^m 1^n mid 2n leq m leq 3n, m,n geq 0 }$?
Problem Detail: I’m not really sure the how you would go about proving this language isn’t regular with the pumping lemma: $L= {0^m 1^n | 2n leq m leq 3n, m,n geq 0 }$ Does this indicate that $S = 2$, Read More …
[Solved]: A polynomial reduction from any NP-complete problem to bounded PCP
Problem Detail: Text books everywhere assume that the Bounded Post Correspondence Problem is NP-complete (no more than $N$ indexes allowed with repetitions). However, nowhere is one shown a simple (as in, something that an undergrad can understand) polynomial time reduction from Read More …
[Solved]: Breadth First Search with cost
Problem Detail: Looking for some tutorials / references that discuss Breadth First Search that takes into consideration the cost of paths, but could not find much information. Could someone refer a tutorial? Asked By : Roberta Rocha Answered By : Carlos Linares López Read More …
[Solved]: Time Complexity of Universal Turing Machine Simulations and the Time Hierarchy Theorem
Problem Detail: I have a little problem to understand the proof of the Time Hierarchy Theorem (Hennie and Stearns, 1966) that ensures the existence of a language acceptable in $U(n)$ but not acceptable in $T(n)$ for any functions $T(n),U(n)$, such that Read More …
