Why is it impossible to iterate over all TMs with $n$ states and $k$ symbols that halt after $m$ steps on $\epsilon$?

Define $ \{\sigma(n,k,m,i)\}_{i=1}^{l_m}$ an ordered set of all TMs with $ n$ states and $ k$ symbols that halt after $ m$ steps on $ \epsilon$

There are $ (2kn)^{kn}$ TMs with $ n$ states and $ k$ symbols, so $ l_m$ is always finite and so is the range of $ m$ .

If we could iterate over $ \sigma$ given $ n,k$ for all $ m,i$ , then we could decide the halting problem:

  1. Get $ n,k$ from input machine
  2. Iterate over $ \sigma$ for all $ m,i$ and check for each one if $ \sigma(n,k,m,i)$ equals the input machine, if they are equal accept.
  3. Reject.

This is odd because It seems very feasible to constract $ \{\sigma(n,k,m,i)\}_{i=1}^{l_m}$ using elementary combinatorics. Even settling on a (computable) combinatorial formula for $ l_m$ for all $ m$ given $ n,k$ will be enough to solve the haling problem since we will know how many machines are there that halt for each $ m$ , and we can simulate one step at a time for all the $ (2kn)^{kn}$ machines and compare each machine that halts with the input machine until reaching $ l_m$ for all $ m$ without a correct comparison and reject.

Is there a fact (independent of it contradicting the Halting problem) that makes it clear why there is no computable combinatorial formula for $ l_m(n,k)$ ? or am I missing some detail here?

Sending different message on a game level after different amounts of time

So, I am working on an interactive game to aid with anxiety management. In one of the gameplay options, the player has to press buttons for a certain amount of time. Only after the required time has lapsed (with the player holding the buttons down), will the avatar move. So, for example the instruction will be "Press the buttons for 20 seconds to move the player". This part is working. As this is an anxiety game, however, I want to incorporate some breathing activity/instruction into the gameplay. I have chosen to use the 4-7-8 second rule, whereby the player breathes in for 4 seconds, holds their breath for 7 seconds and exhales for 8 seconds. I have no idea how to incorporate something like this into my existent game. Any tips or pointers would be appreciated. I understand that a second timer would be needed, but how would that be able to discern between the 4 seconds, 7 seconds and 8 seconds?

Attached is my existent timer script:

using UnityEngine; using System.Collections; using UnityEngine.UI; using UnityEngine.SceneManagement;  public class Timer : MonoBehaviour {     public int timeLeft;     public Text countdownText;     private bool timerStarted;      int start;      public void BeginTimer()     {         StartCoroutine(LoseTime());     }      void Awake()     {         start = timeLeft;     }      public void StopTimer()     {         StopAllCoroutines();         Respawn.Instance.Player2.transform.position = Respawn.Instance.RespawnPoint2.transform.position;         PlayerController.Instance.timerStarted = false;         timeLeft = start;         countdownText.text = "Time Left= " + start;     }      private IEnumerator LoseTime()     {         while (timeLeft > 0)         {             yield return new WaitForSeconds(1);             timeLeft--;             countdownText.text = "Time Left= " + timeLeft;         }                 PlayerController.Instance.Character.GetComponent<Rigidbody2D>().AddForce(PlayerController.Instance.height, ForceMode2D.Impulse);          //SphereController.Instance.Player.GetComponent<Renderer>().material;         print("hi");     }      public void ChangeLevel()     {         SceneManager.LoadScene(SceneManager.GetActiveScene().buildIndex + 1);     } } 

And my playercontroller script:

using System.Collections; using System.Collections.Generic; using UnityEngine; using System.IO.Ports; using UnityEngine.UI;  public class PlayerController : MonoBehaviour {     public static PlayerController Instance { set; get; }     public float Speed;     public Vector2 height;     public float xMax, xMin, yMin, yMax;     public bool buttonPressed = false;      public Rigidbody2D Character;     public Timer timer;     public Rigidbody2D _rigidbody;      public bool timerStarted = false;      private SerialPort sp = new SerialPort("\\.\COM4", 9600);      Animator anim;     string value;     int button;      private void Awake()     {         FetchReferences();         Instance = this;          //print("hi");          if (AvatarChooser.ava == 1)         {             anim = GameObject.FindWithTag("Player").GetComponent<Animator>();             anim.runtimeAnimatorController = Resources.Load<RuntimeAnimatorController>("3");             //print("hi");         }          if (AvatarChooser.ava == 2)         {             anim = GameObject.FindWithTag("Player").GetComponent<Animator>();             anim.runtimeAnimatorController = Resources.Load<RuntimeAnimatorController>("1");         }          if (AvatarChooser.ava == 3)         {             anim = GameObject.FindWithTag("Player").GetComponent<Animator>();             anim.runtimeAnimatorController = Resources.Load<RuntimeAnimatorController>("2");         }     }      [ContextMenu("FetchReferences")]     private void FetchReferences()     {         if (!Character) Character = GameObject.FindWithTag("Player").GetComponent<Rigidbody2D>();         if (!timer) timer = GameObject.Find("Timer").GetComponent<Timer>();     }      private void Start()     {         if (!sp.IsOpen)         {             sp.Open(); // Open          }         sp.ReadTimeout = 1;          //print(AvatarChooser.ava);     }      private void Update()     {         if (sp.IsOpen)         {             try             {                  value = sp.ReadLine(); //Read the information                 button = int.Parse(value);                  if (button == 9)/*(Input.GetKeyDown(KeyCode.Space))*/  //jump                 {                     buttonPressed = true;                     if (!timerStarted)                     {                          timerStarted = true;                         timer.BeginTimer();                     }                 }                 else                 {                      timer.StopTimer();                 }             }             catch (System.Exception)             {              }         }     }       private void FixedUpdate()     {         Character.position = new Vector3                     (                         Mathf.Clamp(GetComponent<Rigidbody2D>().position.x, xMin, xMax),                         Mathf.Clamp(GetComponent<Rigidbody2D>().position.y, yMin, yMax)                     );     }         void OnDisable()     {         sp.Close();     }  } 

Do removed parts of a Druid’s Wild Shape form persist after said Druid exits Wild Shape?

A player wanted to use Wild Shape as an unlimited supply of feathers for our ranger to make his own arrows with and it sparked a discussion on whether or not parts of a Druid that are removed from said Druid’s Wild Shape persist after the Druid is no longer in Wild Shape.

I have been unable to find any rules that either allow or disallow this action. Whereas there are specific rules on what happens to gear the druid is wearing, I have found no statement on what happens to removed physical parts of the Wild Shape form.

I have thought of two reasonable solutions:

  1. Removed pieces of Wild Shape form persist indefinitely. This would make a Druid Indistinguishable from a normal creature until knocked out of druid form and would make the party assassin happy as he now has a reliable fresh supply of Giant venomous snake venom to apply to his daggers.

  2. Removed pieces of wild shape form persist until the Druid leaves Wild Shape. This would avoid the issues of unlimited resources, but raise other questions such as whether blood spilled by the Wild Shape also disappears or whether a creature that has “become poisoned for 1 hour” would stop being poisoned when the Druid is knocked out of that shape because the poison has dissipated with his Wild Shape.

Which (if either) of these lines up with the rules? Or does this fall under DM fiat?

What usually happens to the symmetric (session) key after decrypting an email? Can the key be recovered if changing private keys?

I’ve been preparing for a CISSP exam and was reading about applied cryptography in regard to email.

It’s my understanding that the popular schemes (PGP,S/Mime) use a combination of asymmetric and symmetric cryptography. If I’m reading things correctly, in S/MIME, the message is encrypted using a sender generated symmetric key. In turn, the symmetric key is encrypted using the receiver’s public key.

Encrypted Email

If the receiver changed their private key, they would no longer be able to decrypt the message. However, I was wondering if it was possible to recover the symmetric key from when the email was previously opened?

My guess would be that the email client does not intentionally store the key since that would present a security risk. Just wanted to see if that actually occurs or if there’s something I’m missing.

Ways to heal after casting a spell as an action in the same round


Following this question, I am looking for ways to heal in the same round after casting Beacon of Hope from a Ring of Spell Storing.

I was looking for an abilty like a Divine Channel or an item I could use to heal but didn’t find anything. (and I don’t really know where to search besides Google and the Stackexchange)

Sidenote: I am a level 5 cleric of Qotal but I’m also interested to know how other classes could do.

Is the Change Data Capture __$update_mask value still valid after removing and adding columns to table?

Let’s say I have table I enabled cdc for.

Now, if I want to add some columns to the table and also remove some columns and preserve the CDC data for the old columns, is it going to mess up the update mask values of the historical data?

Based on my tests, dropping columns can leave gaps in the column_id values and new columns receive new column_id values. The column_id field seems to work like an identity field for columns.

So, even if I re-enable cdc for a table after removing & adding columns, the column ids of new columns should be assigned new numbers therefore the masks for historic data should still work, of course as long as I have all the columns that were ever added to the table stored somewhere (cdc.captured_columns contains only the current captured columns).


Redirect to Invoice page after checkout in woocommerce

I have a scenario where in I need to redirect to invoice page after checkout in woocommerce. Avoiding going to payment gatway. I have two type of shipping Flat Rate and Pick at Store. when I select pick at store option no need to make the payment online. Instead it should redirect to invoice page. How do I redirect to invoice page without payment gateway?

Should I be concerned about websites emailing me my plaintext password after signing up? [duplicate]

In multiple instances lately, I have received the plaintext passwords I entered(not given to me) emailed to me after signing up. The sites in question have been legitimate small businesses, so I suspected it was a default setting. Is this something I as a user should be worried about? In other words, are they not only storing my password in plaintext but sharing it with my mail provider? Here is a link to one example screenshot, too large to fit in the post.

Which of the available options for downtime from XGtE would give the most money after one week?

In the "Downtime Revisited" section of Xanathar’s Guide to Everything, pages 123-134, it gives you various suggestions with what to do with a week of downtime. My character is being given a week of downtime and they need to make as much money as they can within this week.

Which of the available options would give the most money after one week?

Some thought/restrictions (although answers can still mention these excluded options alongside the best for my case if they wish):

  • Crime: My character isn’t really built as a rogue, and my DM may well require me to have a relevant background, like Criminal, to qualify for this downtime option, so this one’s out.
  • Gambling: This can go well, or badly (that’s why it’s called gambling), but I don’t have that much money to begin with, so although it’s probably the best option if you have lots to start out with and are happy to risk it (as the amount you can make scales with how much you put down, assuming you win), it wouldn’t really help me much as the risk isn’t worth the reward when I don’t have much to start with.
  • Pit Fighting: Obviously, all PCs can fight, since D&D is a combat-centric game, but I’m not a combative class, I’m a warlock who’s trying to go for more of a "summoner" playstyle, so this probably won’t be my strong suit. Then again, it appears to be "nothing lost, nothing gained" if I lose, so if might be the best one for me, unless the others are better?
  • I was considering just going with the "Work" option, and hoping I roll well enough to get that extra 25gp, but the Pit Fighting option already outpaces that even if I only roll well once out of three times, so I’m guessing that Work isn’t much good after all…

So to clarify: I’m excluding Crime and Gambling as I don’t think they’ll be appropriate, and I’m looking for an option that tops Pit Fighting, which appears to be the best one at a glance for making money quickly.