## #P=NP: All satisfying solutions are valid answers by programs for NP

In fact, the implication looks like an equivalence too.

All satisfying solutions to a boolean formula
are valid answers by programs for NP
is equivalent to saying
the class #P equals the class NP.

Any agreement? Looks trivial. However, complexity classes are untrivial, so… negating both sides of the equivalence also produces an equivalence: Not all solutions are valid is equivalent to #P!=NP.

I have a program for counting solutions to boolean formulas, and after some years of experience, I observed that SAT coNP and #P are roughly equivalent in time complexity. I have published previously a related result called #P=#Q, where the number of satisfying assignments equals the number of valid quantifications of any original boolean formula (Satisfiability 2002, Introduction to Qspace). My program runs fast on small to moderate sizes, and when #P is linear, I can decide all qbfs of the original formula.

My theoretical position is:
coNP=NP=#P=#Q=qbf=allQBFs=?Exp
with #P=#Q being the central thesis.

source code for program bob is available, send me email at gmail, pehoushek1. Sincerely, Daniel Pehoushek, 1983 GREs: 2380/2400

## How to represent JavaScript programs on paper?

At work I’m developing a JavaScript library and often I have the need to represent on paper the classes that I’m building and their relationship in order to explain something to collagues.

What’s the best way to do that? I know UML butmaybe you know a better design technique for JavaScript and dynamic programming in general.

hello everyone.

i want to start marketing adult Affiliate Programs, because i saw that the pay out is very high, and i wanted to ask the Community members what is the best way to start market it (a niche site, ppc)? and if someone can recommend me a good adult Affiliate Programs to start with a one that is Reliable.

## What is the current status of parallel or concurrent programs in the Curry-Howard isomorphism?

In Girard’s Proofs and Types we can read :

From an algorithmic viewpoint, the sequent calculus has no Curry-Howard isomorphism, because of the multitude of ways of writing the same proof. This prevents us from using it as a typed $\lambda$ -calculus, although we glimpse some deep structure of this kind, probably linked with parallelism.

Proofs and Types, J.Y Girard (Page 28)

From the viewpoint of computer science, it gives a new approach to questions of laziness, side effects and memory allocation [GirLaf, Laf87, Laf88] with promising applications to parallelism.

Proofs and Types, J.Y Girard (Page 149, written by Yves Lafont)

How are parallel programs linked to the Curry-Howard isomorphism ? What are the current thoughts about that ?

I have a script, that I want to run when I start my Windows 10 computer. It’s intend is to restrict my usage of the computer and it will shutdown the computer, if I use the computer to much.

At the moment I added the script to the autostart-queue of my computer.

The problem is, when someone else starts the computer after me Windows starts all my autostart programs including the script. This means, that those other users are kicked out although, the script is in my startup queue not in theirs.

Is their any to start the script automatically after login not after startup?

## Why does Pressing Ctrl cause new tab to open sometimes and has some weird effects in other programs?

I am using ubuntu 16.04 in Vivobook ASUS. Sometimes ctrl command opens new tab in my browser. I think it is not about my browser since it has different weird effect in other programs too like in R where it shifts the working script tab to the right sometimes. I can manage to make it back by pressing fn+numlock but it can come again. I am tired of it.

## Linux on Dex – Can you install additional programs? R? Vim?

Linux on Dex is on an Arm processor, not Intel processor. Does this mean I can’t install most normal programs? If you have Linux on Dex could you try and install these two programs, run them, and confirm this will work? I know it just came out, but would like to know before laying out a grand on a Samsung Galaxy Note 9.

R Statistical Package

apt-get update apt-get install r-base R 

Vim Editor

sudo apt-get update sudo apt-get install vim vim new_project.c 

And to quit Vim press Esc then press :. The cursor should appear at the lower left corner of the screen beside a colon prompt. Enter the following q! and Vim will quit.

## When are quadratic integer programs “easy to solve”?

Let $$N_i=\{0,1,\dots,\bar{n}_i\}$$ and define $$N=N_1\times \dots \times N_I$$. I want to maximize $$f$$ on $$N$$. $$f$$ has the following form $$f(n) = \sum_i A_i n_i -\sum_i \sum_{j\neq i} B_{ij} (n_i-n_j)^2$$ where $$A_i\geq 0$$ and $$B_{ij}\geq 0$$ for all $$i,j$$. Note that $$f$$ is concave when defined on $$\mathbb{R}^I$$.

I know that integer programing is in general a hard problem but I would like to find nontrivial conditions on $$A$$ and $$B$$ such that this problem is easy to solve. By easy to solve I mean that there is a procedure that is fast and that is guaranteed to find the global maximum.

### What I have tried

I have tried the following way of solving the problem. Define the mapping $$T$$ for which the $$i$$th element is defined as $$(Tn)_i=\arg\max_{\tilde{n}_i\in N_i} f\left( \left\{ n_1,\dots,\tilde{n}_i,\dots,n_I\right\}\right)$$ and iterate on $$T$$ until convergence. This is essentially a coordinate ascent algorithm but in a discrete space.

A few remarks:

1. We can look at the fixed points of $$T$$. The vector $$n^*$$ that maximizes $$f$$ is obviously a fixed point of $$T$$ (can’t improve by deviating in any dimensions) but there might be multiple fixed point.
2. The mapping $$T$$ is monotone in the sense that $$n\geq n’$$ implies $$T(n)\geq T(n’)$$. As a result we can use Tarski’s fixed point theorem to show that the (non empty) set of fixed point is a lattice. We can find a lower bound of that set by iterating on $$T$$ from $$(0,\dots,0)$$ and an upper bound by iterating from $$(\bar{n}_1,\dots,\bar{n}_I)$$. If both procedures end up on the same vector then there is a unique fixed point and it must be $$n^*$$.
3. When it works that procedure is quite fast numerically but I don’t know what conditions on $$A$$ and $$B$$ are needed for it to work.
4. Under some conditions, $$T$$ might be a contraction mapping which would guarantee uniqueness but I haven’t made much progress along that path yet.

Any help is appreciated! In particular, if somebody has a good reference on these problems that would be useful.

## How to multiply time programs use through the sleep() system call?

how to multiply time a program waits for the sleep() system call so that when it asks to sleep 1µs it actually pause 2µs and when it ask 3 minutes it actually sleeps 6 minutes rather than the asked time ?

This is something easy on Linux PC as it’s possible to trick the Bogomips kernel parameter to an incorrect value using hibernate and modifying Bios settings.

The rationale is timings is the reason why enemies in Video Games mostly react at roughly the same speed across different hardware speeds and operating systems.

So how perform the same on android ?

## Running programs as sudo doesnot work

Uubuntu 18.04

Installing tools and other using command line with sudo works perfectly. example: sudo apt install … works perfectly. Running tools and programs via the command line as sudo doesn’t work at all. Running the same programs and tools as normal user works perfectly. Example: start gtkwave as normal user makes the gtkwave gui pop up. Start gtkwave as sudo, asks for password and then ends in: sudo: gtkwave: command not found.

Must say that some tools invoked on the command line as sudo work flawless. example: I can start atom form the command line as normal user and as sudo.

Is this maybe because the tools/programs not running as sudo are not installed in the common Linux folders like /bin or /usr/bin but as programs under /opt (these are add to the path and have necessary environments set)?

Anybody any idea why this happens?