Create machines from a non-regular grammar

I have two grammars:

 L → ε | aLcLc
 L → ε | aLcLc | LL 

These two grammars are the same, but the first one is regular, creating a regular language and finite automata. Instead, the second is not regular, but may produce a regular language.
To prove this, I want to create two different machines: the first one should be a correct machine, and if the second can not be created, the language is not regular. Are all these statements correct?
If so, can someone help me to set up these two machines? Thanks a lot!

Updates – Different kernel versions on different machines

I have 2 different machines, with the same OS version and the same source list.

$ lsb_release -a
LSB Version:    core-9.20170808ubuntu1-noarch:security-9.20170808ubuntu1-noarch
Distributor ID: Ubuntu
Description:    Ubuntu 18.04.3 LTS
Release:    18.04
Codename:   bionic

I update my packages with the following commands pc-1 and pc-2:

$ sudo apt update
<...>
$ sudo apt -y upgrade
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Calculating upgrade... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

However, I get different kernel versions for each machine:

pc-1 $ uname -r
5.0.0-25-generic

and

pc-2 $ uname -r
4.15.0-58-generic

Why is that how and how can I safely update pc-2 on the latest generic kernel with official repos and not ppas?

Is there a way to debug / print the kernel selection logic in apt?

Google Cloud Platform – GCP – Terraform does not create a specific number of virtual machines

Here's a tf script I'm running to make debugging easier:

# Credentials
provider "google" {
  credentials = "${var.credentials}"
  project = "${var.project}"
  region  = "${var.region}"
}

# Regional MIG
resource "google_compute_instance_group_manager" "rmig" {
  name               = "${var.rmig_name}"
  instance_template  = "${google_compute_instance_template.cit.self_link}"
  base_instance_name = "${var.base_instance_name}"
  #region             = "${var.region}"
  zone               = "${var.zone}"
  target_size        = 7

  named_port {
    name = "http"
    port = 80
  }

  named_port {
    name = "https"
    port = 443
  }
}

# Template creation
resource "google_compute_instance_template" "cit" {
  name_prefix = "${var.prefix}"
  description = "${var.desc}"
  project = "${var.project}"
  region  = "${var.region}"
  tags = "${var.tags}"
  instance_description = "${var.desc_inst}"
  machine_type = "${var.machine_type}"
  can_ip_forward = false // Whether to allow sending and receiving of packets with non-matching source or destination IPs. This defaults to false.

  scheduling {
    automatic_restart   = true
    on_host_maintenance = "MIGRATE"
  }

  // Create a new boot disk from an image (Lets use one created by Packer)
  disk {
    source_image = "${var.source_image}"
    auto_delete  = true
    boot = true
  }

  network_interface {
    network = "${var.network}"
    # Give a Public IP to instance(s)
    access_config {
      // Ephemeral IP
    }
  }

  service_account {
    scopes = ("userinfo-email", "compute-ro", "storage-ro")
  }

  lifecycle {
    create_before_destroy = true
  }

I specify 7 virtual machines to be created from my template. In fact, GCP actually creates 7 virtual machines, which is correct, but 4 of them are off, and a few minutes later, the powered-off virtual machines are deleted leaving me with only 3 powered-on virtual machines.

When I try to start a powered-off VM through the GCP UI, I get the error:

"Booting VM instance" apache-d2dv "failed." Error: Google Compute
The engine is not yet ready for use in the project. It may take several
Minutes if Google Compute Engine has just been activated or is the case
You used Google Compute Engine for the first time in your project. "

Is this a problem with GCP (in which case do I have to switch providers) or with my TF code?

turing machines – Which of the following languages ​​is crucial?

I have a question about the decidability of the following languages:
1. L = {| from ∈ L (M) and M only accept w with | w | > = 10}
2. L = {| M accept only a limited number of words}
3. L = {| L (M) = ∅ ∨ L (M) = Σ *}

For the first, I think it undecidable, because it may be that the Turing machine does not stop after checking to see if ab is an element of L (M).
I would be happy about any explanation.

turing machines – A condition for $ emptyset neq S subset RE $, under the $ L_S notin RE $

I read some lecture notes on computational theory and after citing and proving the sentence: $ emptyset in S Rightarrow L_S = { langle M rangle: L (M) in S } notin RE $ it stands that $ emptyset in S $ is not a sufficient condition, i. $ L_S notin RE $ does not give way $ emptyset in S $by giving the counterexample $ L _ { Sigma ^ *} notin RE $ , However, it means that there is a necessary and sufficient condition under which $ L_S notin RE $, I searched for this condition in Sipser's book but did not find it. I would be very happy to receive a reference for this condition.


Edit: Given the answer from @dkaeae, I would like to know what the stronger feature is that can be derived from a non-trivial one $ S subset RE $ in the case $ L_S notin RE $,

Probability – Two machines produce 30%, 70% materials with 3%, 5% faulty units, probably a randomly selected material is faulty

If I have no idea how to start. Two machines A, B produce 30.70% material for one company respectively 3%, 5% defective units.
a] What is the probability that a material of the entire output is faulty?
b] Probability that the defective material was produced by machine A.
c] Probability that this faulty material was produced by Machine B.

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virtual machines – will Jenkins crash the system? if it was not used for a week

I'm so curious if Jenkins will crash the system / operating systems if it's not used for a month or a week.

Actually, I hosted Jenkins on a remote server for the CICD approach, but for some reason, I have not been used for several weeks, but after the organization escalated that Jenkins crashed the system? it was shown in the list when the system was scanned from the end.]

Will Jenkins like these topics?
To be honest, I can not believe this information, so I am able to identify the problems?

What is the class of machines with stacks and unlimited memory that can only be addressed by instant addresses?

Suppose we have a machine with an infinite stack and an infinite number of "registers", but no arbitrary memory access, and its data is separate from the code.

I am sure that these are at least pushdown machines, but I am not quite sure if we can bring this machine up to linear automation. The upper bound is obviously the Turing machine (because pushdown machines with an extra stack have the same capabilities as the Turing machine).

The only way to save data using these machines is to move them to the stack (push #3 – Move content from register 3 to the stack or push 3 – push 3 on the stack) or use mov command with at least one register specification (mov #1, 1 Register 1 = 1, mov #2, #1, Register 2 = register 1). We can also assume that loop operations are present, along with addition or subtraction.

The questions are:

  • What is the class of these machines?
  • If these machines are not a linear-limited automation or Turing machine, you must complete the following steps to create one:
    • Add another batch
    • Allow arbitrary memory access

turing machines – How to detect endless loops in linear limited machines (LBA)?

The machine $ M $ is deterministic. This means that if $ M $ is in a specific configuration $ c $Then there is a single fixed configuration $ c & # 39; $ (determined by the rules of $ M $) to which the execution of a step leads. If $ M $ ever reached the configuration $ c $ again then the configuration $ c & # 39; $ will follow, no matter what. Therefore, if the calculation of $ M $ causes configurations to be accepted $ c_1, dots, c_n $ and $ c_n = c_1 $, then $ M $ Repeats the loop $ c_1, ldots, c_n $ unlimited.