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Show/prove that $UPrime = \{ |^n : n ∈ N \space is \space prime\}$ is in P

I have this question to solve. According to my understanding, it basically requires a turing machine that outputs lines on the tape, with the number of the lines being any prime number.

My idea is to take the AKS test’s conclusion and making a case that since, calculating primes is a problem that can be solved in polynomial time complexity as already proven by AKS, hence this problem is also in P.

Is this the right way? what would be a more formal/mathematical way of expressing this if it is?

MS SQL running out of Disk Space – can FileGroups be used to free up some space?


Problem

We have a Sql Server 2014 with a 1TB attached disk (on Azure) that’s running out of disk space. We have about 20GB’s left (maybe a few weeks of space). As such, we need to move some data off the CURRENT disk and onto a NEW disk.

Details

Server:

Microsoft SQL Server 2014 - 12.0.2548.0 (X64)      Jun  8 2015 11:08:03      Copyright (c) Microsoft Corporation     Web Edition (64-bit) on Windows NT 6.3 <X64> (Build 9600: ) (Hypervisor) 

MS-SQL 2014 is installed onto a classic Azure VM. This VM is in a classic VNET. The storage DISKS are also classic. As such, we couldn’t just expand the existing disk. MS-Support said that we need to update all of these, if we wish to leverage the modern Azure Storage to allow disk resizing, using the newer SSD disk, etc. TL;DR; we can’t take this offline for hours including all the other subsystems that communicate with the VM via IP address. Now, don’t turn this into a flame-fest .. this is what we’ve been given to work with and will need to fix all of this up later.

So right now, an idea what to try and leverage FILEGROUPS and to move one or more tables into a FILEGROUP and push this FILEGROUP onto another DISK which we have attached.

So the questions here are:

  • Is this a really really crazy and lame idea, first of all?
  • If it’s crap but OK, then will using FILEGROUPS actually move the data from the CURRENT disk onto the NEW disk (which frees up some disk space on the nearly full CURRENT DISK)?
  • If this is still possible, does moving these tables mean the data is locked/unavailable … which means were still back to our initial problem 🙁
  • What about logs? Moving this data means the logs just get a copy of this? (we are doing hourly and weekly backups, I believe).

It’s ok if the data is small, but here’s a quick look at some of our tables…

enter image description here

That first table is massive (with respect to the rest of the data). 750GB ish.

I was thinking of moving maybe the 2nd, 3rd of 4th line, in the result image. Remember how I said the infrastructure is all on OLD classic stuff? This means the HD’s are old and slow so copying data could take some time also.

As an example, I just tried to copy the .mdf‘s (this DB has 1 main mdf and 2 other small ones) from OLD over to NEW disks. that had a quick ETA of 24 hours.

Having the site offline for a few hours is totally acceptable. We can take stuff offline when our customers are asleep. but … 24 hours .. that hurts. The 24 hour idea was a simple test for:

  • Create new 2TB Disk (if possible)
  • turn off sql server.
  • copy mdf + log files to new disk. (24 hours or so)
  • point filegroups from old location to new location
  • start sql server again.

Now, we’re open to ideas and I know that stack exchange is not a site for ‘opinions’ so I’m trying to keep this on target with a suggested answer and to get feedback on it … but we’re open to other solutions to reduce the offline time.

So – can anyone help please?

Estimating number of points in 1D space

There are some arbitrary-chosen points in 1D space. What needs to be found is the approximate number of them without counting all of them. It is possible to choose some coordinates (numbers) and for each one there are two numbers returned – the distances to the closest points to the left and to the right.

I’m looking for some sources on how to solve such problem efficiently so any papers, generalizations or similar problems are needed.

[ Physics ] Open Question : Why do the Star Trek writers think that stopping engines will stop forward momentum in space?

Shouldn’t they at least know that they’d have to reverse thrusters to give the equal and opposite force to stop forward momentum? Shouldn’t someone writing for one of the premier scifi franchises know this basic fact? Verisimilitude is the hallmark of good fiction writing.

What is the relative return point of the Banishment spell? (The ‘space it left’)

I’m well aware I can just choose. I’m just looking for discussion.

When a creature returns from the Banishment spell, it returns at the ‘space it left’.

How do you play the reference point to this space?

IE if it is banished from a galloping horse, after a minute the horse will have travelled a long way. Is the return point on the horse? Or where the horse was when the Banishment occurred?

Same thing with being banished from a moving ship. Does the creature return on the ship or on the water where the ship was?

Recover lost space from failed create table from another table

AWS RDS Postgres 9.6 – I was performing this on a table of 1.7billion rows: CREATE TABLE raw_data_smaller AS SELECT id,updated_dt::date, status, price FROM raw_data; I realized it was running short on space so I modified… adding 1TB. Looked like it would still need more, but before it finished storage-optimization (and allowing me to add more) ran out of space. But even though the CREATE TABLE as stopped, and that table is not in the list, the 3TB of space is gone. How do I get the space back?

Why does $L = \{ 0^n 1^n \space | \space n \in \mathbb{N} \}$ belong to $\mathcal{P}$?

My professor said that the non-regular language $ L_{1} = \{ 0^n 1^n \space | \space n \in \mathbb{N} \}$ belongs to $ \mathcal{P}$ . I do understand that all regular languages belong to $ \mathcal{P}$ as it’s easy to determine and so can be computed in $ \mathcal{O}(n^k)$ , but why do most non-regular languages not belong to $ \mathcal{P}$ but $ L_{1}$ does? Is it also possible to give an example of a language $ L$ that does not belong to P?