Does a regular expression exist for any number that contains no more than two 5s and no 6 twice in a row?

For example, a valid number would be 6165156 and an invalid number would be 1566515.

I have tried many times to construct a finite state machine for this with no success, which leads me to believe the language is not regular. However, I am unsure how to formally prove this if that is indeed the case. I tried applying the pumping lemma but I am not completely sure how to apply it to this particular language.

Any help is appreciated!

What in-universe reasons exist that explain why druid can use metal weapons but not wear metal armour?

In 5e, we are told that the druid shouldn’t wear metal armour:

Armor: Light armor, medium armor, shields (druids will not wear armor or use shields made of metal)

I believe this was true in older editions of D&D as well; "druids will not wear armor or use shields made of metal". Certainly the below quote seems to imply this…

In the 2016 sage advice, we are told that druids choose not to wear metal armour:

What happens if a druid wears metal armor? The druid explodes.

Well, not actually. Druids have a taboo against wearing metal armor and wielding a metal shield. The taboo has been part of the class’s story since the class first appeared in Eldritch Wizardry (1976) and the original Player’s Handbook (1978). The idea is that druids prefer to be protected by animal skins, wood, and other natural materials that aren’t the worked metal that is associated with civilization. Druids don’t lack the ability to wear metal armor. They choose not to wear it. This choice is part of their identity as a mystical order. Think of it in these terms: a vegetarian can eat meat, but the vegetarian chooses not to.

This question is not about what happens if druids wear metal armour, or whether certain druids might choose to wear it despite not being a common choice among druids.

My question is: why is there not a similar taboo around druids making use of metal weapons? Is there anything in any published material (ideally from 5e but I suspect that previous editions probably have more to say about this than 5e) that explains why druids are generally happy to metal weapons, despite the fact that they typically choose not to wear metal armour (or use metal shields)?


Just a reminder that this is not a designer-reasons question as I’m interested in lore-based answers, in-universe explanations, not any designer’s reasons from any edition as to why it was decided from a gameplay-based or mechanical point of view. I’m interested in the lore reasons only.


Related:

  • What would be the side effects on a Druid of wearing metal armor?
  • If I multiclass from ranger into Druid, can I still wear metal armor?

What opportunities exist in D&D 5e in order to turn into beasts, while maintaining personality and mental characteristics?

What opportunities exist in D&D 5e in order to turn into beasts, while maintaining personality and mental characteristics (Intelligence, Wisdom and not necessary Charisma)?

As far as I can see, one of the obvious solutions is Wild Shape. Are there any other options?

What creatures exist (besides the Githzerai) that associate psionics with anything besides Intelligence?

My understanding of psionics in D&D is that it is usually tied to Intelligence.

Going by player classes, the UA Mystic class was Intelligence-based, and going by monsters, many of them who are capable of psionics appear to be Intelligence-based as well, such as the Mind Flayers (MM, p. 222):

Innate Spellcasting (Psionics). The mind flayer’s innate spellcasting ability is Intelligence

However, I am aware that the Githzerai, both the playable race and the monsters, use Wisdom instead.

The playable race, from MToF (p. 96):

Githzerai Psionics.Wisdom is your spellcasting ability for these spells.

And an example of one of the "monsters", a Githzerai Monk (MM, p. 161):

Innate Spellcasting (Psionics). The githzerai’s innate spellcasting ability is Wisdom

Even the Githyanki (both playable race and monsters) use Intelligence, like most of the other psionic creatures in D&D. As far as I can tell, it’s just the Githzerai who are different in this regard.

I really want to ask "why do the Githzerai use Wisdom for psionics when everyone else uses Intelligence?", but that’s off-topic due to being a designer-reasons question. So instead, I will check my assumption, since I’m assuming that the Githzerai are the only ones who buck this trend, simply because I’ve not managed to find any further examples (i.e. "all swans are white").

Question

Are there any other creatures who have psionic abilities (and the ability must be called out, either in lore or with the psionics tag, as being psionic; not just any old source of psychic damage or similar effects) that are not tied to Intelligence? If so, what creatures don’t follow this pattern, and what do they use instead of Intelligence (if anything)? Or is it literally just the Githzerai who buck this trend?


My understanding is based on D&D 5e, but I’d be interested in answers that consider psionics throughout all editions of D&D if that wouldn’t be asking too much (and if such a question would even make sense, given how the rules change between editions). If such a question would be too broad, or wouldn’t make sense, I’m happy to reduce the scope back to "just D&D 5e".

How to show that these two disjoint sets $A$ and $B$ exist

I came across this problem which asks to show the existence of two disjoint Turing-recognizable sets $ A$ and $ B$ such that no decidable set $ C$ can separate them…

In this case, a set $ C$ is said to separate $ A$ and $ B$ if $ A \subseteq C$ and $ B \subseteq \overline{C}$ … If only $ A$ is Turing-recognizable, then we could easily set $ A$ to be $ A_{TM}$ and $ B$ as $ \overline{A_{TM}}$ . However, in this case both $ A$ and $ B$ are Turing-recognizable …. I think that $ A$ and $ B$ should be constructed using diagonalization, but could not think of a way to do it … Any help ?

Do any single-cell organisms exist that approximate NP-hard problems within a factor better than $1/2$ $log$2?

I’ve seen on Wikipedia; that set covering cannot be approximated in polynomial time to within a factor mentioned above. Unless $ NP$ has quasipoly-time algorithms.

Now, this must pertain to classical algorithms and does not mention any approximation algorithms that may only work in nature.

(eg. Things like Amoebas solving $ TSP$ problems)

  • Do any single-cell organisms show any promise in solving $ NP$ -hard problems in polynomial-time?

  • Or approximating them better than any known classical algorithms?

Do negative Hit Points exist in D&D 5e?

Say that a character has 5 HP remaining and is dealt 10 damage from an attack. Of course, 5 – 10 = -5, so the character has dropped below 0 Hit Points and follows the rules for making death saving throws (provided they didn’t get dealt enough damage for instant death). However, it’s not clear to us if the character remains at -5 Hit Points or if they bounce back up to 0 Hit Points (like many rules in 5e, knowledge of past editions may be a hindrance to interpreting them).

If negative Hit Points exist, then characters will take longer to recover naturally (since stable characters recover at a rate of 1 HP per 1d4 hours). Also, a natural 20 on a death saving throw, which recovers one Hit Point, would not make them instantly conscious. Finally, it would mean that instant death is a greater possibility, as you need less to reach the threshold if you are attacked again.

However if negative Hit Points do not exist and characters bounce up to 0 after crossing the 0 HP threshold, then characters will always regain 1 HP and become conscious after waiting 1d4 hours or rolling a natural 20 on a death saving throw. Also, this would mean that instant death is far less likely because someone who attacks an unconscious character would always need to deal maximum HP damage or they don’t kill you (and if they don’t, then I guess their damage means nothing, which seems rather odd).

Unfortunately, the example provided with the basic rules isn’t helpful because it describes someone taking enough damage for instant death, but not someone who got less than that. Furthermore, the rules describe “Dropping to 0 Hit Points”, but not “Dropping Below 0 Hit Points” and seems to omit what happens when you take more damage than the HP you have remaining, but less than enough for Instant Death. Our group spent a while debating this when we played from the Starter Edition and we weren’t sure given that some previous versions of D&D had them while others didn’t. So do negative hit points exist or do characters “bounce up to 0 HP”?

What archfey exist in Eberron lore that would make a suitable warlock patron?

I’m planning on making an Archfey warlock for an upcoming Eberron game. To flesh out my character’s backstory, I want to know more about what kind of "fey" entities such a warlock might form a pact with.

For context, the character’s backstory is that they are a Valenar elf who’s ancestor that he has to emulate was an "Eldritch Knight" or similar, some kind of battlemage anyway, except that my character isn’t very strong or smart (STR and INT are his dump stats), so he instead formed a pact with an archfey being to make up the difference, becoming a Pact of the Blade warlock so that he could better emulate his ancestor.

The reason I’ve picked the Archfey archetype is because the Valenar seems to be rather connected with fey, at least considering the various "Valenar xxx" animals listed in Eberron: Rising from the Last War.

I can of course work with my DM to just "invent" an archfey if need be, but I wanted first to see if there are any existing named archfey within any Eberron lore (from any edition of D&D if 5e doesn’t have anything), and bonus points if that archfey is associated with the Valenar elves at all.

Finding the lengths at which cycles exist in a graph in parallel

I’m trying to find an algorithm that can find the lengths of simple cycles in an undirected graph in parallel that benefits strongly enough from it’s parallelization to be practically more efficient than what I’m currently using to find simple cycles in an undirected graph.

Basically if a graph has n nodes, I need to know if there is a simple cycle of each possible length between 2 and n in the graph. I’m currently using https://www.boost.org/doc/libs/1_55_0/boost/graph/hawick_circuits.hpp because it performs massively better than any other implementation I’ve found of simple cycle algorithms. However, it seems that NP-hard graph problems that rely on backtracking tend to be very tricky to parallelize.

I have access to computers that would allow me to benefit greatly from distributing the problem across CPU cores, but I’m failing to find papers or past discussions of people parallelizing this particular problem space.