Minimum pumping length of concatenation of two languages

there’s this small part of my homework that I just can’t figure out.

Let us denote $ p(L)$ as the minimum pumping length of some language $ L$ . I’m supposed to find two regular languages $ A,B$ so that

$ $ p(AB)=p(A)+p(B) $ $

But whatever I try, I can only find languages so that

$ $ p(AB) < p(A)+p(B) $ $

I’ve been sitting at this the whole day and I’m just going in circles. Can someone please give me a hint?

Regular languages, automata

I want to ask about the definition of regular languages. My book says there has to exist a deterministic finite automaton that recognizes it. Does this mean the finite automaton recognizes exactly this language and nothing else or it can recognize possibly some other words not in the language?

Finding a finite automata that accepts a language that is the combination of two other languages with their own automata

I’m told that we have two DFA one A and one B both on alphabet $ \sum$ .

I’m then told to define a DFA (5-tuple representation) with this condition {w | w = $ a_i b_i$ $ a_k b_k$ and all the $ a \in A$ and all the $ b \in B$ }

Also 1 $ \leq$ i $ \leq$ k and $ a_i \in \sum$ and $ b_i \in \sum$ .

However I simply do not understand how I’m supposed to do this. Simply put my confusion is what $ w = a_i b_i$ mean. Is it concatenation? Does it mean that the word $ w$ is the concatenation of a with b?

How useful are the exotic languages?

I’ve chosen the Haunted One background for my new half-orc blood hunter. I get to pick an exotic language (Abyssal, Celestial, Deep Speech, Draconic, Infernal, Primordial, Sylvan, or Undercommon), but other than Draconic (which I’ve only ever used as a dragonborn, to talk privately with other members of my party), I have never come across any of them before.

How often do you encounter an NPC that uses them, and how likely is it that I’d end up using any of them? Do any lend themselves to being more useful than any others?

I’m yet to flesh out my backstory, perhaps that will guide my choice, but before I do that it would be good to know more about the languages.

Enumeration of a class of languages

Can you enumerate a class of languages in such a way that the description of every language/ machine enumerated encodes where it was in the enumeration?

Ex:if you are given the description of the bth machine/language enumerated you could quickly check, by some tag or marker in the description of the bth machine / language, that it was indeed the bth machine/language in the enumeration by an enumerator E.

Can you modify any enumerator for a class of languages so that it does this? Or can such an enumerator E be rigged up to do this for any enumerable class of languages?

To give context, my goal is for a verifier to accept, as one part of its input, the machine/language enumerated, and be able to see, quickly, what position that machine/language was in the enumeration by the enumerator E.

Thank you!

Web with two languages. The urls with the /es/ do not index

Good morning,

I have launched a website with English and Spanish languages. I’ve done it using WPML, but I’m having a lot of problems indexing and ranking the Spanish URLs, which appear in the URL the /es/.

Google Search Console is declaring all URLS like as “Duplicate, submitted URL not selected as canonical”

I really need these pages, despite being translations of the English version, to also index and rank keywords.

Any solutions? Thank you!

What’s the deal with alignment languages?

In early D&D, there was the concept of an “alignment language.”

The original “little brown book” D&D says only:

Law, Chaos and Neutrality also have common languages spoken by each respectively.

The Holmes basic rules, which come between “brown book” and Moldvay say:

Lawful good, lawful evil, chaotic good, chaotic evil, and neutrality also have common languages spoken by each respectively. One can attempt to communicate through the common tongue, language particular to a creature class, or one of the divisional languages (lawful good, etc.). While not understanding the language, creatures who speak a divisional tongue will recognize a hostile one and attack.

Moldvay D&D says:

Dungeons & Dragons, Basic Rules, page B11

Alignment Languages

Each alignment has a secret language of passwords, hand signals, and other body motions. Player characters and intelligent monsters will always know their alignment languages. They will also recognize when another alignment language is being spoken, but will not understand it. Alignment languages are not written down, nor may they be learned unless a character changes alignment. When this happens, the character forgets the old alignment language and starts using the new one immediately.


So much of Dungeons and Dragons was very generic “sword and sorcery” fantasy that these rules always stuck out to me as an extremely sore thumb, or like one of those snails that has been infected by a fungus and begins to pulsate in random colors. What the heck is going on here?

So, alignment languages show up pretty early in D&D’s history. Every intelligent being that is on the side of Law can communicate. Every intelligent being that has no particular feelings about Law can, too. If they experience a profound change in their feelings about this, they can no longer communicate with the people they used to. It isn’t clear how much communication is possible in an alignment language, since Moldvay describes it as “passwords, hand signals, and other body motions.”

In AD&D 1E, though, there is no such limitation:

Advanced Dungeons & Dragons, page 34

Character Languages

In addition to the common tongue, all intelligent creatures able to converse in speech use special languages particular to their alignment. These alignment languages are: Chaotic Evil, Chaotic Good, Chaotic Neutral, lawful Evil, Lawful Good, Lawful Neutral, Neutral Evil, Neutral Good, and Neutrality. The alignment of your character will dictate which language he or she speaks, for only one alignment dialect can be used by a character (cf. CHARACTER CLASSES, The Assassin). If a character changes alignment, the previously known longuage is no longer able to be spoken by him or her.

That cross-reference to the assassin class is there because assassins alone can learn the languages of other alignments. Probably not all of them, though, because now there are nine instead of three.

In AD&D 2E, the alignment language seems to have been silently dropped, and never spoken of again as far as I know.

When I was ten and played AD&D, the idea of alignment languages struck me as incomprehensible, and today even though I have come to love almost everything about basic and early-Advanced D&D, alignment languages still seem incomprehensible, weird, and unexplained.

What I want to know is this: how were (or are) alignment languages put to use, described, and conceived of in actual play ? So far, my use of them has always been “pretend they do not exist.” I am curious as to how others view and address them.

Also: where did this bizarre idea come from? It smacks of being lifted from some fantasy book, but I can’t recall ever reading anything like it.