Arbitrary Turing machine run time analysis on the empty word

Consider $ L = \{ \langle M,n \rangle : M $ accpets $ \epsilon $ in less than $ T(n)$ steps$ \}$

This language is decidable because we can simulate $ M$ on $ \epsilon$ and accept if it accepts and reject if it rejects or passed more than $ T(n)$ steps.

I am interested in the time bounds of a decider of $ L$ , can we find a decider to do so in $ o(T(n))$ time? $ O(T(n)log(n))$ is achieved by simulation time bounds (and maybe even $ O(T(n))$ , I’ve seen somewhere that a linear time simulation can be achieved) but is it possible to do so in some $ o(T(n))$ time? since we are dealing with a constant word, it might have a better time complexity than a general simulation time.

Associative mapped cache, word addressable

I have an associative mapped cache with 10 tag bits and an offset of 7bits.

What is the size of each main memory block in words(word addressable) and main memory size in words?

i worked it out as: block size would 2^7bits. main memory would be 2^17bits.

the issue I am facing is, how do I get them to be word addressable with this much information given. I have managed to get the above result in byte-addressable. Please correct me if i am wrong.

Can you cast healing word with charisma as a paladin cleric multiclass if healing word is prepared as cleric?

I am going to play a life domain cleric paladin multiclass with high charisma. Since life domain cleric already has healing word as a prepared spell, can I cast it with my charisma or do I need to prepare healing word again with paladin to cast it with charisma?

How to determine minimum word length of regular language

Given a regular language $ L$ and a regular expression $ r$ with $ L=L(r)$ . Is it possible to determine the minimum length of words of $ L(r)$ by the structure of $ r$ ?

A straightforward example:

Let’s say we have a regular expression $ r=aac^*aa$ , then $ L(R) = \{aaaa, aacaa, aaccaa, \dots, aac^naa\}$ . To determine the minimal length I would erase everything that is postfixed with $ *$ , leaving $ r’=aaaa$ . Now I would count the concatenations and add 1, which would yield in this example, not unsurprisingly, a minimum length of 4.

Is there a general approach to do this for more complex expressions?

Functionally, how does Power Word Kill work?

I was just reading this answer, which introduced me to the Power Word Kill spell:

You utter a word of power that can compel one creature you can see within range to die instantly. If the creature you choose has 100 hit points or fewer, it dies. Otherwise, the spell has no effect (101 hp or more).

Functionally, how does this spell work? If I’m understanding this correctly, a PC can speak a word, and if the target has less than 100hp, they instantly are killed without the chance to save. My reason for asking is that this seems extremely overpowered, to the point where it could be used to kill deities or high-level bosses with little effort (especially those who rely less on having high HP and more on dealing extremely high points of damage – Moon Druids come to mind here).

While I recognize that the DnD system does allow for extremely powerful spells (cough cough wish cough cough), this one in particular seems to stand out.

Thus, functionally, how does Power Word: Kill actually work?

Note: I am not asking whether or not the community subjectively finds this spell overpowered. Rather, I am attempting to confirm how this spell works in practice, in order to decide for myself if it is overpowered.

To add some more specific touch-points to guide a potential answer:

  • Are any saves permitted?
  • Does the spell need to be heard by the target, or seen being cast?
  • How might resistances or type-immunity play a role (if any)?

The purpose of this question is to confirm that this spell works in the way I am imagining, which while to me seems overpowered, if I am incorrect may not be the case.

Microsoft Word Security Warning for Signed VBA Project

I am attempting to setup signed VBA Projects so that I can find the right balance between security and useability.

Currently my end users are instructed to just hit “Enable Content” on Microsoft Office to allow running of the Macro’s.

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Obviously this is a security issue as it’s a blind approval, they should in fact be told to never hit “Enable Content” and the goal is that Word will automatically run the documents because the VBA Projects are digitally signed.

I have made a cert using “SelfCert.exe”. Imported it into the “Trusted Root”. It shows as trused. I opened VB Edited and applied this to my document, changed Word Trust Security Center settings to “Disable all except digitally Signed”. But, I still get the warning and can’t figure it out. Is this a glitch? Am I doing something wrong? Looking for help from somebody with experience with this issue.

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How to mark a tooltip-containing word in a paragraph?

I have a sentence in which one word has a tooltip. The data in the tooltip is supplemental and putting it into the main UI isn’t required.

However, how can I mark the word to notify the user that it has a tooltip? I’ve tried marking the word with an underline and blue color, but it looks too much like a link (which it isn’t).

Below is the image of what it looks like now:

Text with tooltip


When I am uploading a Word Document in Document Library – Custom Columns values are getting blank

I have uploaded the Word document on SharePoint Document Library (Modern Site), my Library has following columns:

  • Title

  • ADDS

  • LBB

  • Category

Step 1: After uploading the file for the first time, I have filled the values in these columns on SharePoint.

Step 2: Again, I have uploaded the same file, now above columns values got blank.

Issue with Title > I can understand this…. Title is MS Word property as well and it will be overwritten (As per this – Document Properties not carry to new version).

But why my other custom columns values are getting blank???

Note: This issue is coming only for MS Office files (DOC, PPT, XLS, etc.). However it’s working as expected for other file formats – .pdf, .jpg, .zip, etc

Attaching word document

When I attach a word document in outlook 2013 it does not attach properly. The file name becomes attachment49193829, with no file extention, and the reciever cannot open it. The attachment does not have a word icon but instead a blank page with top corner folded. Any ideas why it wont attach? Cheers.