Problem Detail: I found this problem while I was reading an ACM problem and it is about dynamic programming. The problem says that you have a square matrix $ntimes n$ filled with 1’s or 0’s, like this: $$begin{bmatrix} 1 &1 &1 Read More …
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[Solved]: 3-SAT where variables occur equally many times as a positive literal and as a negative literal
Problem Detail: Let $phi$ be a 3-CNF formula over variables $x_1,x_2,ldots,x_n$. Every variable $x_i$, $i in [n]$, occurs equally many times as a positive literal and as a negative literal in $phi$. Is it NP-complete to decide the satisfiability of such Read More …
[Solved]: Automated geometric theorem-proving using synthetic methods
Problem Detail: This question is about geometric theorem proving and is inspired by this Math.SE post. Currently, Euclidean-geometric theorem provers, as referred to in the post, use coordinate geometry to convert a geometry problem into a set of algebraic equations. Why Read More …
[Solved]: Comparing random access and sequential access
Problem Detail: Assume that we choose randomly $k$ distinct numbers $N_1$, $dots$, $N_k$ in ${1, dots, k}$ and we have a file of $k$ parts. We have these two cases : We read (or write) sequentially from part $1$ to part Read More …
[Solved]: Lower bound for finding majority element in a sorted array
Problem Detail: Suppose $A$ is a sorted array with $n$ elements. I want to know whether we can determine if there are majority elements in $A$ with time complexity $O(1)$. Recall that a majority element of $A$ is an element which Read More …
[Solved]: Will floating point code return the same arithmetical results on two different computers?
Problem Detail: Say I am using boost or the built-in float or double mathematical libraries of my C++ compiler. I distribute the program. Will the execution of my C++ program on different machines given different floating point results given that the Read More …
[Solved]: Why don’t modern SAT solvers use the notion of a “watched clause”, in the same way they use the notion of a “watched literal”?
Problem Detail: Modern SAT solvers use the notion of “watched literals”: when a value is chosen for a literal $l$, the solver only checks whether that falsifies clauses with $l$ in them if $l$ is one of the watched literals in Read More …
[Solved]: How can GIF compression be lossless if the maximum # of colors is 256?
Problem Detail: I’m reading “Computer Science Made Simple” by V. Anton Spraul, and in the chapter about Graphics, he describes GIF files as follows: A GIF file uses lossless compression to store an image with a maximum of 256 different colors. Read More …
[Solved]: How is a witness found in a proof of $mathsf{NP} subseteq mathsf{P}/log implies mathsf{P} = mathsf{NP}$?
Problem Detail: I’m having a hard time understanding the actual proof of this proposition: $qquad mathsf{NP} subseteq mathsf{P}/log implies mathsf{P} = mathsf{NP}$ The sketch of the proof is on slides 6-8 of this PDF. So I let $L in mathsf{NP}$. That Read More …
[Solved]: Reducing a problem to Halt
Problem Detail: I’m reviewing for a computability test, and my professor has not provided solutions to his practice questions. I came up with a “solution” to this problem, but it really seems like my answer is wrong (since I call upon Read More …
