Problem Detail: My understanding is that Karp many-one reductions are more general than Levin many-one reductions, and that Levin many-one reductions must allow for the number of certificates for a problem $A$ reduced to $B$ to be recovered from a single Read More …
Category: Uncategorized
[Solved]: Is every undecidable language reducible to any other undecidable language?
Problem Detail: For the undecidable languages I have seen so far , I am able to give a reduction from one language to other . Is it the case that every undecidable language is reducible to every other undecidable language? If Read More …
[Solved]: Simple Pushdown Automaton
Problem Detail: I’m currently learning about PDAs and their power when constructing them from Context-Free Grammars, however I’m still unsure of how to properly construct a CFG, and then a PDA from that CFG. In the book, Formal Languages, Automata, and Read More …
[Solved]: Are there some real-world optimization problems with very cheap objective functions?
Problem Detail: Many real world optimization tasks (especially black box optimization) have objective functions, which are quite expensive to evaluate. For example to find the optimal shape of an airplane wing, a computer model of the wing needs to be constructed Read More …
[Solved]: Is it theoretically exist a computer that never affected by computer virus?
Problem Detail: Is it theoretically exist a computer that never affected by computer virus? just wonder if there could be a revolution on the computer? Asked By : Victor Answered By : babou Do you mean “that cannot be affected” or “that was Read More …
[Solved]: Why is $sum_{j=0}^{lfloorlog (n-1)rfloor}2^j$ in $Theta (n)$?
Problem Detail: I am trying to understand summation for amortization analysis of a hash-table from a MIT lecture video (at time 16:09). Although you guys don’t have to go and look at the video, I feel that the summation he does Read More …
[Solved]: How many possible assignments does a CNF sentence have?
Problem Detail: I’m having some trouble understanding the following: When we look at satisfiability problems in conjunctive normal form, an underconstrained problem is one with relatively few clauses constraining the variables. For eg. here is a randomly generated 3-CNF sentence with Read More …
[Solved]: Is it more effective to vote for a woman?
Problem Detail: A certain political party wants to encourage women to participate in their primary elections, so they decide, that the 4th position is reserved for a woman. That is, if there is no woman in the top 4 positions, then Read More …
[Solved]: Why don’t we emphasize “length of input string” when considering time complexity of sorting algorithms?
Problem Detail: The knapsack problem is $O(c,n)$ where $c$ is the capacity of knapsack and $n$ is the number of items. Yet it’s exponential because the size of the input is $log(c)$. However, why don’t we emphasize length of input in Read More …
[Solved]: Selecting random points at general position
Problem Detail: How will you find a random collection of $n$ points in the plane, all with integer coordinates in a specified range (e.g. -1000 to 1000), such that no 3 of them are on the same line? The following algorithm Read More …
