Show that infinite decidable sets $A$ and $B$ exist

I am stuck in this problem, so any help is appreciated. The problem asks to show that there exists decidable sets $ A$ and $ B$ such that $ A \leq_{m}^{p} B$ but $ B \not \leq_{m}^{p} A$ , and that $ A$ , $ B$ and $ \bar{A}$ and $ \bar{B}$ are infinite.

Here, $ \leq_{m}^{p}$ refers to many-one polynomial time reducibility…. I have a hunch that this may have something to do with letting $ A$ be a decidable set such that $ A \in EXP$ , but $ B \in P$ , so that the reduction cannot be done in polynomial time.

What range categories exist for spells?

The SRD gives us a helpful list of possible ranges for spells: Personal, Touch, Close, Medium, Long, Unlimited, and Range Expressed in Feet. However, this is clearly not a comprehensive list of all of the possible range categories in the game. For example, Persistent Spell’s text claims that “Spells with a fixed or personal range can have their duration increased to 24 hours”. This is despite, to my knowledge, “fixed range” not being a term that is defined in game or obviously understandable in plain English (e.g. this question shows one potential source of confusion).

This leads me to my question: What range categories does the game acknowledge, what are their definitions, and where are these definitions found or derived from?

What lore justifications exist for tieflings with blue skin?

Tieflings (in 5e, at least) have either “human skin colour”, red skin, or somewhere in between. I think 4e changed how tieflings look between 2/3/3.5e and 5e, standardising the red skin/Asmodeus look, but I believe that the tiefling’s skin colour has always been within this range from the little I know of the previous editions.

From the 5e tiefing player race description, Infernal Bloodline section (PHB, p. 42):

Their skin tones cover the full range of human coloration, but also include various shades of red.

All official art I’ve seen of tieflings in 5e (and, again, the little I’ve seen of previous editions) backs this up, showing mostly red tieflings.


However, from Tiefling Variants sidebar (Sword Coast Adventurer’s Guide, p. 118):

Rather than having the physical characteristics described in the Player’s Handbook, choose 1d4+1 following features: small horns; fangs or sharp teeth; a forked tongue; catlike eyes; six fingers on each hand; goatlike legs; cloven hoofs; a forked tail; leathery or scaly skin; red or dark blue skin; cast no shadow or reflection; exude a smell of brimstone.

So there is a rule here that allows tieflings to have blue skin. Unfortunately, this is the most I’ve seen in 5e material that refers to tieflings having blue skin.

What lore justifications exist for why a tiefling might have blue skin as opposed to the more usual red or “human skin colour”?

I’ve heard some people (online and IRL) say that it relates to the different bloodlines as per the options presented in Mordenkainen’s Tome of Foes, but reading that section of that book, it doesn’t mention skin colour at all, so I’m not sure where this interpretation came from but it doesn’t appear to be RAW.

I’m looking for official lore, ideally from 5e but lore from previous editions is welcome too (I’m guessing AD&D Planescape stuff might shed some light on this?). I’m looking for lore from any official setting, but if that’s not specific enough, let’s say Forgotten Realms.


Related:

  • Is there a way to determine what physical traits your character could have based on their Diabolic bloodline? (closely related, but it asks “what appearances are for which fiendish bloodline”, whereas I’m after any lore explanation for skin tone specifically)
  • Can a tiefling have permanent ivory white skin? (loosely related, as this question was just asking to justify a skin tone choice without much emphasis on lore explanation)

Why do Invalid Host header errors exist, what are attackers trying to achieve?

I have recently launched a new django based api, and quite quickly, I started to receive INVALID_HOST_HEADER SOME RANDOM URL errors. My understanding is that this is caused by somebody manually changing the HOST header, or proxying my API through some other domain.

This is probably a basic question, but what is the point? What are they trying to achieve? Presumably it’s not a regular MITM attack, because it would be easy enough to correct the HOST header on its way out of the middle server, and they’re not doing so.

Can there exist Tables with no Non-Prime Attributes? If so, are they always normalised to 3NF?


Can there exist a table with no non-prime attributes?

Here is an example of a table which I believe has no non-prime attributes:

I came to this conclusion because the list of attributes in the relation is [id, tag_desc_id, name] and the list of candidate keys is [{id}, {tag_desc_id, name}]. There are no attributes in the list of attributes that are in none of the candidate keys. Thus, there are no non-prime attributes.

Is my reasoning correct?

If so, is it normalised to 3NF?

The criteria for 3NF is:

  • 2NF

  • Every non-prime attribute of R is non-transitively dependent on every key of R

There are no non-prime attributes, thus 3NF is satisfied

The criteria for 2NF is:

  • 1NF

  • Every non-prime attribute is (…)

Again, there are no non-prime attributes.

Is this true generally?

For any table, assuming the table has a primary key id as above (and so 1NF is satisfied), and the table has no non-prime attributes, is it always the case that the table is normalised to the third normal form (3NF)?

What methods exist to get your AC higher than 20 without magic items?

I was poking around answering for this question about the highest AC possible for a sorcerer and noticed something odd.

It doesn’t seem to be possible except in the case of the Barbarian to naturally get your AC over 20 without the use of magic items.

Is there a way that I’m missing or is this a relatively hard and fast rule (with the noted exception of the Barbarian).

The Barbarian’s exception lies in the fact that he gets to add Dex and Con to his AC, and his Level 20 capstone is a +4 bonus to CON (to a max of 24, which I’ll assume here), which gives him a potential AC of 24 (Dex 5, Con 7, shield +2).

(Note: I’m looking for permanent solutions; if you want to delve into spells, they should have duration similar to mage armor and not require concentration.)

Someone downloaded my game but it failed on Game Start due to code that doesnt exist

As stated in the title, they get the following error:

 ############################################################################################  FATAL ERROR in  action number 1  of Other Event: Game Start  for object obj_music_controller:   ds_map_find_value argument 1 incorrect type (undefined) expecting a Number (YYGI32)  at gml_Script_scr_checkLastLoggedInJson  ############################################################################################  --------------------------------------------------------------------------------------------  stack frame is  gml_Script_scr_checkLastLoggedInJson (line -1)  gml_Object_obj_music_controller_Other_2  

The function ds_map_find_value() is not being called in the script scr_checkLastLoggedInJson(). (Even if it was, how could it be happening at line -1?)

Nor is it called in the Game Start event of the obj_music_controller object. I also checked every use of ds_map_find_value() in the entire game and they are all fine.

Furthermore, this is only happening with 1 person. And they have tried uninstalling it and re-downloading. Even after i uploaded a new version of the game, this still happened to them and only them.

Does a 2-party decentralized consensus protocol exist?

Assume there are 2 people in a conversation. Each one may support a given stance on an issue (the support is binary, either agreement=1, or disagreement=0). Both want to find more like-minded individuals, without revealing their (potentially incriminating) stance to someone who does not support it. We can assume that neither one of them wants to be misrepresenting themselves, so they will not lie about their stance, but otherwise if possible, both will attempt to find out the stance of their counterparty without giving out their own.

In technical terms: 2 parties (called A, B), each knowing 1 boolean value (v_A, v_B), want to compute a shared value v_A AND v_B, without revealing the underlying values to each other. By the properties of AND, it is unavoidable that if v_A is true, A is able to deduce v_B from the result, but in the opposite case (v_A is false), this isn’t possible (as requested).

In a centralized scenario, this could be easily solved by both parties providing the values to a trusted third party, which computes the result and sends it back to both parties, but TTP might not always be available.

Is it possible to construct a protocol that achieves this goal without a third party, under the constraints mentioned at the end of first paragraph?

I know undergraduate math reasonably well, with some basics in homomorphic encryption, signature algorithms, and a few articles about zero knowledge proofs. Feel free to leave pointers to more literature, I’m be happy to learn what’s necessary on my own.

P.S.: I’m aware that the practical cryptographic use of such a protocol is very limited, as neither of the parties can be forced to provide correct value (and always providing 1 leads to discovery of the other value), and trying to incriminate them by publishing it, even if undeniable, would reveal your own support.

Does there exist an algorithm to generate the production rules of CFG, given a sample production?

Lets say, we provide the algorithm a set of tokens.

e.g.

x + y - z x - x - x 

It will then try to generate a CFG which fits all the provided examples

S -> S O T | T T -> x | y | z O -> + | - 

It feels like a data compression problem but I could be wrong.

Does anybody know any existing literature or a starting point to solve this problem?

Does this problem have a name? What should I Google?

Force create foreign key even if reference does not exist

I have two tables foo and bar, bar has column a that references foo.id as a foreign key. When creating table bar before foo, the error column "a" referenced in foreign key constraint does not exist is given. This is obvious and intended. However, the creation of these two tables are handled by two different entities that of which I cannot control. It’s guaranteed that no data will be added to either table until both are successfully created, but the creation itself may happen out-of-order. Is there a way to force the creation of bar even though foo does not exist?