Is the empty string and some words of even length are elements of this set?

$ L = \{w \in \{a,b\}^*| \text{the first, the middle, and the last characters of $ w$ are identical}\}$ .

I have my answers, but I need confirmation:

Is the empty string $ \epsilon \in L$ ? Yes. Reason: there is no first, middle, or last character to break the rule.

Words of even length, assuming the first and last characters of them are identical, again, must be in $ L$ , as there is no middle character to break the rule in such words.

This is in the context of theory of computation by the way.

Breaking Wifi password knowing its length of 8 [A-Z] alpha (upper-case) characters using Hashcat

I got the WPA handshake, now it’s turn to crack the password using Hashcat. First, I wanted to make a wordlist of passwords [A-Z] the length of 8, but Crunch (the tool in Kali Linux) said it will take 1TB of storage that I don’t have available, so I gave up that way. Is there any way to generate passwords (example: ABCDEFGH) and delete them after its use one by one, during the cracking process?

How long does it take to crack the password with i5-3320M CPU using Hashcat? Is there any other way you recommend?

Regular expression for a palindrome of finite length?

I have a language $ $ L = \{ww^R, w \in \{ab\}^5\}$ $

I know this is a regular language because it is finite (since w can only be of length 5). I want to prove it’s a regular language, so I’d create a regular expression for it.

Theoretically, my regular expression could be the union of all strings in the language, but is there a concise way to express this rather than writing all possible strings out?

How to make a dynamic/variable length physics based rope in Unreal?

So I have followed several tutorials on making a physics based rope. I have found success but, it seems like a waste of time to keep creating a mesh and calibrating it for each rope that I create. I really need a more streamlined approach to be able to create them faster as I have a lot of different ropes of varying lengths and diameter.

It seems to be rather inefficient to create a skeletal mesh for each rope that I create. It would be really nice if I could create a rope of say 1 unit and then add multiple of these units together to create a longer one that has the correct physics or at least very little manual calibration needed.

This doesn’t need to be done at runtime but, I’d like the finished asset to be able to do it all inside of Unreal Editor.

Has anyone done anything similar to this or can point me in a generally good direction? I really don’t know where to start with this one. Any help would be greatly appreciated.

Are NP proofs limited to polynomial length?

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is “yes”, have proofs verifiable in polynomial time by a deterministic Turing machine.

The proofs for an NP decision problem are verified in polynomial time.

Does this imply the proofs are at most polynomial length?

“Well you have to read the whole input. If the input is longer than polynomial, then the time is greater than polynomial.”

The decision problem “Is the first bit of the input a 0?” can be solved in constant time and space – without reading the whole input.

Therefore, perhaps some NP problem has candidate proofs that are longer than polynomial length but checked in polynomial time.

Longest Even Length Palindromic Substring (with unique adjacent characters except for the center 2 letters)

You are given a string S containing lowercase English characters. You need to find the length of the largest subsequence of S that satisfies the following pattern: X1,X2,X3…Xn,Xn,…X3,X2,X1 where Xi is some character of S. The only constraint is that no adjacent character should be the same except Xn, that is Xi != X(i+1) for all 1<=i< n.

Input: The string: S

Output: The integer: 2n

Constraint: 1<=|S|<=10^3

Sample input 1: “acdbdea”

Sample output 1: 4

Explanation: “adda” is the longest subsequence following the given pattern.

Sample input 2: “abbacdeedc”

Sample output 2: 6

Explanation: “cdeedc” is the longest subsequence following the given pattern.

Sample input 3: “taker”

Sample output 3: 0

Explanation: No subsequence follows the given pattern.

This question was asked in a coding interview and I didn’t know how to solve it. I understood how to find longest palindromic sub sequence but don’t know how to implement the unique adjacent character part. Please help. pseudo code is fine

Counting the number of binary strings of length m with no consecutive 1s (RR). How to improve it?

I am new to Mathematica and I am trying to solve this problem of counting the number of binary strings of a certain length m, as far as no consecutive 1s are there.

For instance m = 3, my recurrence relation should give 5 i.e. 000, 001, 101, 100, 010.

I started like this with initial seeds: n > 0; a[ 1] = 1, a[2] = 3, a[3] = 5 and then in RSolve I did:

enter image description here

Is there a better way to improve it so that I can use the output in a plot? Currently, I cannot as my solution says it cannot be used as function.


How much can changelings alter the length of specific body parts?

Like with disguise self, changelings can alter their total height by 1 foot. So they could make both their legs 1 foot shorter, and that would work. In theory, they could even turn both their legs into little stubs, with a 1-inch-tall torso, as long as they elongate their neck to be about 5 feet long.

But what if a changeling wanted to take on the guise of a certain pirate, who’s missing a single leg? In other words, leave their total height the same and keep one leg the same length, but make the other leg into a little stub. That’s a change of more than 1 foot (erm, so to speak), but it isn’t explicitly a change to their height, since their remaining leg determines how tall they stand.

That much can also be asked about the spell, but changelings add on the twist that the alterations are actual physical changes. So is there any difference in the situations between changing the length of a leg, and changing the length of body parts that don’t contribute to height?

That is to say, is there anything stopping a changeling from growing out 50 feet of hair so the party can cut it off and use it as a rope? Or, similarly, causing their arm/fingers to become 50 feet long to manipulate items from the opposite side of a room? Or causing their tail to grow from 0 inches to 50 feet for no particular reason other than giving me another body part example for presumably the same rule?

And then, what about doing all of the above at the same time?

image included to demonstrate what exactly I mean

UTF8mb4 MariaDB 10.4 – Max key length is 767 bytes error

I am running MariaDB 10.4. I am trying to setup symmetricDS for database syncing. Some of the tables it creates have fields that are are VARCHAR(255). I know UTF8mb4 can only support up to VARCHAR(191)

I know I can setup my database to be UTF8 and this problem goes away. But it is my understanding that is not ideal solution. I can’t change the tables/fields that symmetricDS is creating.

I have read some other posts about this, since there are many. But haven’t seen anything above MariaDB 10.2 which I believe I read that things have changed with the engines past 10.2. So I just want to see if it is all still relevant.

Is there any way this can be resolved, while staying with UTF8mb4? Or does it even matter and just go to UTF8?