## Basic complexity theory (in Oracle Separation of BQP and PH)

I have some basic questions about complexity theory that came up when I tried to understand the result by Raz and Tal that BQP$$^O\nsubseteq$$ PH$$^O$$. Aaronsons paper was helpful, but I still have some questions left.

1. Raz and Tal derive Corollary 1.5 from 1.4 “by the relation between black-box separations and oracle separations”, but aren’t those the same thing? I thought the following all mean the same:

• black-box model
• oracle model
• relative/relativized problem
• query complexity

It would make more sense to me if Corollary 1.5 follows from 1.4 by the relation between promise problems and decision problems in the black-box model.

2. I am not sure how to interpret the fact that there is randomness in the problem. I think of a class such as BPP as languages solvable by a regular Turing machine with access to a random tape, which can make an error with a constant probability over its random bits. However we need to consider the worst case instantiation of the problem (right?). For a language to be in PH, there needs to be a PH-machine (without access to randomness) that does not fail on any input. Now for any oracle-output coming from one distribution there is a non-zero probability that it was actually generated by the other distribution, so the PH-machine will be wrong sometimes. Why is that argument not sufficient to show that the problem is not in PH (or any other “zero-error” class for that matter)?

3. What exactly is meant by an AC$$^0$$ circuit with access to an oracle? I’ve seen this described as “a circuit with access to the oracle’s truth table”, which I could understand if the oracle solved a decision problem $$f: \{0,1\}^n \rightarrow \{0,1\}$$, then the circuit input nodes are $$x_i = f(i)$$ for $$i \leq 2^n$$. However, here the oracle samples from one of two distributions on $$\{\pm 1\}^{2N}$$ and the circuit is defined as $$A: \{\pm 1\}^{2N} \rightarrow \{\pm 1\}$$. Does that mean the circuit only gets access to a single query output?

## Basic math operations with SUM() – unexpected values

we had this problem: updated version of MariaDB Columnstore from 1.2.2 to 1.2.4 and nonsense started.

We have these columns col1, col2 both are DECIMAL(15,3) there was already working query to calculate these two columns (see alias A) and this wasn’t calculating right when col2 had zero sum – after db update. Alias B was first approach which didn’t help. And C was solution for proper working.

I want to know explanation why this happened and what caused this behaviour.

SELECT id, SUM(col1) AS c1, SUM(col2) AS c2, SUM(col1 - col2) AS A, SUM(CAST(col1 AS DOUBLE) - CAST(col2 AS DOUBLE)) AS B, SUM(CAST(col1 AS DECIMAL(15,3)) - CAST(col2 AS DECIMAL(15,3))) AS C FROM table GROUP BY id

1.2.2:

+----+----------+--------+-----------+ | id |    c1    |   c2   |     A     | +----+----------+--------+-----------+ |  1 | 1199.940 |  0.000 |  1199.940 | |  2 |  979.860 | 69.990 |   909.870 | +----+----------+--------+-----------+

1.2.4 with extra SUMs

+----+----------+--------+-----------------------+---------+-----------+ | id |    c1    |   c2   |           A           |    B    |     C     | +----+----------+--------+-----------------------+---------+-----------+ |  1 | 1199.940 |  0.000 | -9223372036853575.868 |       0 |  1199.940 | |  2 |  979.860 | 69.990 |               909.870 |  909.87 |   909.870 | +----+----------+--------+-----------------------+---------+-----------+

## Can ‘Microsoft basic data’ partition be deleted?

I am want to uninstall ubuntu(16.04), from my dual boot system and probably reinstall ubuntu or install kali(dual boot it with windows). I want to allocate more space to the already existing windows. I have 10 partitions and I want to figure out if any of these partitions can be freed(not necessary for windows) so that I can increase the disk space allocated to windows as well as allocate more storage to Kali.

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## COMUNICACIÓN SERIAL VISUAL BASIC AUTOMATIZADA

tengo un programilla hecho en visual basic mediante el cual puedo conectarme a un sensor tipo arduino y enviar y recibir datos, el tema es que necesito que el programa me envíe una cadena de datos al sensor cada cierto tiempo, ya que el sensor me devuelve sus datos mediante el comando enviado, ¿Cómo podría hacerlo? La idea es que el programa muestre la salida de los datos al enviarse el comando automáticamente, dejando solo visible el textbox de salida de datos cada minuto

## basic jQuery plugin template

I would like to know if I’m writing a plugin for jquery correctly. I followed the official guide and also added some tweaks that I’ve found from various sources over time.

While this works perfectly, I don’t know if I’m doing something wrong.

This is the sample:

(function($) { var plugin = "my_plugin_name"; var methods = { init : function(user_settings) { return this.each(function(index) { if(!$  (this).hasClass("plugin_class"))                 {                     $(this).addClass("plugin_class"); var$  this = $(this); var data =$  this.data(plugin);                      if(!data)                     {                         var default_settings = {                             optionA: "abc",                             optionB: 123,                             optionB: true                         };                          if(user_settings)                         {                             $.extend(true, default_settings, user_settings); }$  this.data(plugin,                         {                             "settings": default_settings                         });                     }                      privateMethod($this); } }); }, exposedMethodX : function(value) //$  (selector).my_plugin_name("exposedMethodX", true)         {             console.log(value)         }     };      $.fn[plugin] = function(method) { if(methods[method]) { return methods[method].apply(this, Array.prototype.slice.call(arguments, 1)); } else if(typeof method === "object" || !method) { return methods.init.apply(this, arguments); } else { alert("Method " + method + " does not exist"); } }; function privateMethod(obj) { console.log(obj.data(plugin).settings); } })(jQuery); ## Cracking the code interview: Problem 1 .6 basic string compression I created a github repository containing my code solutions for some of the exercises proposed in the book, I updated my solution for the problem 1.6 at https://github.com/dariosicily/cracking-the-code-interview-solutions/blob/master/chap1/compression.c . Here’s the code: #include <stdio.h> #include <string.h> /* a function that compress the original string and store the compressed * string in compress ex. aabcccccaaa will become a2blc5a3. If the * compressed string is longer than the original it returns the * original string*/ const char *compression(const char *original, char *compress) { size_t len, i, j, nc; /*memorize the first char of original in compress*/ char previous = original[0]; len = strlen(original); nc = 1; for (i = 1, j = 0; i < len; ++i) { if (original[i] == previous) { ++nc; } else { compress[j++] = previous; compress[j++] = nc + '0'; nc = 1; previous = original[i]; } } /* there are characters still in the stream */ compress[j++] = previous; compress[j++] = nc + '0'; compress[j] = ''; if (strlen(compress) >= len) return original; return compress; } int main() { char buffer[20] = {0}; printf("%s\n", compression("aabcccccaaa", buffer)); return 0; } I’m looking for possible improvement of the code or better algorithm to solve the problem, any suggestion is appreciated. ## Getting full Ubuntu after a basic installation I installed Ubuntu 18.04 some time ago on a computer and I don’t remember exactly what I chose, but it must have been something like a basic/minimal installation, because some packages are missing (I had to install libreoffice-gnome for example). I was wondering if it’s possible to install all the other packages I’m missing but that are available in the “full” configuration without completely reinstalling Ubuntu? ## Basic Powershell script strange behaviour I have small script. Which i want test it with “If, else statement”. I have the same value variables but when try to compare it, it gives else condition, but it should give true condition. Below are my vars with results.$  ASE1=Get-Content -path "C:\Program Files\Kratos\Tools\ASE\cnf\_ASE.cnf" | out-string -Stream | Select-String "VERSION"

Version 85

$ASE2=Get-Content -path "C:\ProgramData\Kratos\Tools\NaCl\Files\xASE.cnf"| out-string -Stream | Select-String "VERSION" Version 85 if($ ASE1 -eq \$ ASE2) { echo “equal”} else { echo “not equal”}

This above small script return me “not equal” condition but in true this vars is equal to each other. Do you know what im doing wrong ?