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Example of non-regular context free language L such that prefix(L) is regular

Suppose we have some non-regular context free language L. Suppose we also have language of all prefixes of words in L.

What can be an example of non-regular language L such that language of it’s prefixes is regular (Can be represented by a finite automaton)?

I don’t understand how language of prefixes can ever be regular, since the set of prefixes of a word include the word itself.

For example $ L= a^nb^n$ is my non-regular language. The language of it’s prefixes would include : $ \epsilon,a^n$ where $ n\ge 1$ ,$ a^nb$ where $ n\ge 1$ etc…

But what about b’s ? We need to know how many a’s there were in the first place. Therefore I don’t see how the language of prefixes can be regular.

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What 3.5e feat/spell/skill lets you know if you’re breaking a vow/your god’s rules as a free action?

I am building a D&D 3.5e Saint Cloistered Cleric with a Vow of Poverty and Vow of Peace. In the past two weeks, I ran across a character ability (a skill, feat, spell, alternate class feature, domain ability, or something) that had wording like:

as a free action you can consult your intuition and know whether something is in accord with your god’s will [or breaks a vow, I’m not certain of the exact benefit]

I remember specifically that it was a free action and it let you check the status of an action under consideration. But I’ve spent 3 hours searching the Book of Exalted Deeds, the Player’s Handbook, and Google and can’t locate it.

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Finding a Context- free grammar (CFG) for the language [duplicate]

This question already has an answer here:

  • How to prove that a language is context-free? 2 answers
  • How to convert PDA to CFG 2 answers

I am trying to find a CFG for the language A below. I have spent hours on this but still could not find the answer. I also came up with the idea that this may not a context- free language but there is actually a PDA that recognizes it. I would very much appreciate if anyone can help me with this.

                    A= {0^a 1^b 0^c 1^d | a+b < c+d, a,b,c,d>=1} 

Does poking yourself with a needle with the intend to do damage require the Attack action, or can it be done as a (free) object interaction?

Does poking yourself with a needle hard enough to cause damage require the Attack action, or can it be done as a free object interaction?

This task is certainly no more involved than opening a door, which is the example of an object interaction in the PHB. Also, having your player do an Attack roll for such a trivial thing feels ridiculous. However, this would provide an easy way to sustain your rage when you cannot attack or are not attacked.