## How to leverage the fact that I’m solving 1000’s of very similar SMT instances?

I have a core SMT solver problem consisting of 100,000 bit-vector array clauses, and one 10000-dimensional bit-vector array. Then, my program takes as input k << 100,000 new clauses, and adds them to the core SMT problem. My goal is, for any input of k clauses, to solve the entire problem.

Is there any static optimization or learning I could do on the core problem in order to find a better way to solve each of its siblings? For instance, is there some property of the graph of bit-vector variables being constrained in each clause that I could use as a heuristic for solving the specific instances?

Thanks!

## How come non creatable/destroyable Roblox instances have :Destroy() :Clone() etc?

Roblox has many types of instances. But services and other NonCreatable Instances (ReplicatedStorage, Workspace, etc.) still have methods for creating or destroying. Why? Why do they have :Destroy() and :Clone() methods if they cannot be destroyed or created? What’s the point of inheriting these from the Instance class?

## Is it possible to sync up LMKs in two Thales PayShield 9000 instances>

Basically, when we execute a generate key command such as `A0` then we receive a `key-under-lmk` for future use. What if we have multiple HSMs in a high availability configuration? How would we make sure that all keys-under-LMK mean the same thing to all HSM instances?

The documentation I have doesn’t cover this and I didn’t find anything online about that particular model.

## Can you add your the same modifier to damage rolls multiple times if they come from different instances?

A friend of mine is wanting to do a specific build and as far as I am aware you can not apply a modifier multiple times in this way. Can someone confirm if this is a RAW legal tactic?

Scenario: lv 6 tiefling celestial warlock, assuming 16 charisma

Cast shillelagh to make staff 1d8+cha [source: pact of the tome]

Then cast searing smite for 1d6+cha [source: teifling and celestial warlock’s radiant soul feature to add charisma mod]

A single hit would be 2d8+1d6+9

Do all these instances of charisma modifier stack like this?

## Are there instances in which a character can choose to trade in a spell slot for some negative consequences?

Last night, I DMed a game with only two players, and neither of them had any prior experience with D&D. All in all, it went great, but towards the end, they got into some serious trouble and the druid seemed somewhat surprised by the fact that she had used all of her spell slots. I didn’t want to punish a beginner too hard and the only alternatives appeared to be a near inevitable TPK or some cheesy deus ex machina, so I told her she could try to cast Healing Word despite having used all of her magic power for the day. I let her make a CON save to decide how she could handle the enormous stress of stretching her abilities to such an extend. She rolled quite high, but not extra-ordinarily high, so I decided that she could indeed successfully cast the spell, but that it might backfire later in some way. I haven’t decided the specifics yet and in order to keep it interesting but balanced, I am looking for something similar to this in any official source book.

I’m aware that I’m well into homebrew territory with that ruling, and that this is not the right site to ask for inspiration. This is why I am specifically asking the following:

### Is there any class or racial feature or any item that allows a character with no remaining spell slots to cast a spell of level 1 or higher at the cost of some negative consequence (e.g. taking a level of exhaustion)?

I am not asking for general ways to simply cast spells without expiring a spell slot. There has to be some immediate trade-off. Taking 18 wizard levels in order to gain access to Spell Mastery can of course be seen as quite a trade-off, but I hope it is obvious that this is not what I am looking for.

## Algorithm to output all instances of stable matching

So the Gale-Shapley algorithm is just one way to output one stable matching instance. Is there any algorithm that can allow us to output all stable matching solutions ? Thanks

## Medusa / THC Hydra on multiple instances

Is it possible to distribute the login tries in THC Hydra / Medusa in multiple computers?

For example

``hydra -l root -x 6:6:A1 127.0.0.1 ssh ``

That equals to 2176782336 login tries, how can I distribute this job in several computers to make it faster?

Any possible code reference or topic related to this kind of procedure? Thanks in advance

## Can an Order of the Mutant Blood Hunter benefit from multiple instances of the same Mutagen at once?

The Order of the Mutant archetype of the Blood Hunter class has the ability to use mutagens to increase ability scores.

The rule for using mutagens reads in part:

As a bonus action you can consume a single mutagen, and the effects and side effects last until you finish a short or long rest, unless otherwise specified. While one or more mutagens are affecting you, you can use an action to focus and flush the toxins from your system, ending the effects and side effects of all mutagens.

So a Blood Hunter can clearly have more than one mutagen in effect at the same time, but could the Blood Hunter have the same mutagen in effect simultaneously?

Specifically, could a Blood Hunter use two instances of the Potency mutagen to increase her strength score to 26? I’m not sure if the rules for combining spells applies since the ability isn’t a spell (or even described as being magic).

## Any known instances of friendliness or friendship between opposing dragons?

As known dragons are not necessarily enemies of each other despite different alignments.

What I am wondering is are there any known instances of friendliness or friendship between chromatic and metallic dragons?

## An Exact Method for Solving Small Instances of XORSAT

I have a couple of small instances for XORSAT for which I am to design and implement an exact method. However, there are a few catches. It is guaranteed that there always exists and answer but I need to find the one solution with the minimal (non-zero) number of TRUE variables.

As I understand, XORSAT can apparently be solved in polynomial time through the Gaussian Elimination method but I simply cannot apply the special conditions of this problem (the minimal number of TRUE variables) and I’m wondering if I could potentially get some help on that.

The instances of XORSAT that I have are not completely random, they all consist of a number of variables that if XOR’d together will always yield FALSE. I.e., all of the clauses are in the form of $$x_1 \oplus x_2 \oplus … \oplus x_i = 0$$ which would translate into the equation $$x_1 + x_2 + … + x_i = 0\space(mod 2)$$.

At first, I tried to apply a greedy method, taking the two most repeated variables in all of the clauses and forcing the value TRUE on them, then propagating their values through all of the clauses and repeating the same method on the remaining unsatisfied clauses but that was fundamentally flawed.

Any help is tremendously appreciated.