Does Improved armor and armor stacks?

It might be a simple question:

Does 1- point Customization Aegis Improved Armor

  • The astral suit thickens and strengthens, increasing the aegis’s Armor bonus by +1. This customization can be taken once for every five levels the aegis possesses and stacks with any Armor bonus granted from the astral suit itself. The aegis must be at least 5th level before selecting this customization.

and normal armor such as Half-plate armor stacks? So at 2 level result: AC 8+1=9

Thanks

Psionic talent modifiers stacks?

If you choose "Unlocked Talent", you choose 5 "psionic talents" (also named 0-level psionic powers) then if you have enough power points to spend, you can activate "Precognition, Greater", then "Inertial Armor", then "Thicken Skin", then "Force field". Each of these add Armor Class modifiers and sometime Saving Throws modifiers, can they stack?

Implementing an efficent priority queue using only stacks

Is it possible to implement an efficient priority queue (as efficient as a heap) only using the stack data structure?

The usual efficiency for a priority queue which is implemented using a heap is :

  • get min – $ O(1)$
  • extract min – $ O(\log n)$
  • add – $ O(\log n)$

Would it be possible to do something with the same complexity using only stacks?

Can Aegis stacks 2 improved damage?

I have a cascade of questions relative to customization points and their use but i THINK all-in-one question is better, but if you want I can divide that as well as you prefer, meanwhile: Can a 2 level Aegis with 14 power points (a long story) and 4 customization points stacks improved damage (2cp) and improved damage again (2+2 cp)? So, because is 2hand weapon fighter (not the class), he can stacks +6 on damage (due to the previous), right? Can he do this with astral skin? (yes I think) Can, if he do this with astral armor, stacks Brawn (as free customization) + Improved damage (as free customization) + Improved damage (paying 2 cp) + Improved damage (paying 2 cp) as total = +2+3+3+3= +11 damage? It seems Yes.

Is equal spacing in Stacks in design tools useful?

More and more design tools are implementing some form of stacked groups that allow you to automatically set vertical spacing between the items in the group. The way this is implemented is that a single value for the spacing between all elements in the group is set and applied.

I’m questioning the validity of this. When I have a few elements stacked vertically the spacing between those elements is most likely not all going to be the same. Therefore I don’t see the point of having a single value spacing in a vertical stack. Am I an exception here? Or am I missing something?

Example of a vertical stack:

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A push-down automaton with two stacks which is equivalent to a linear-bounded automaton

It is known that a PDA with two stacks is equivalent to a TM.

On the other hand a PDA with one stack is capable to recognise only context-free languages.

Hence there is a kind of a gap between the class of PDA with one stack and the class of PDA with two stacks which should be capable to recognise only context-sensitive languages.

I feel like it should be already an examined question, but I couldn’t find an answer: what restrictions should we apply to a PDA with two stacks in order to make it equivalent to a Linear-bounded automaton?

Generate all permutations of 1 to n with i stacks

Assume we have i stacks. the possible actions are:

  1. push to first stack form input
  2. pop from stack i and push it to stack i+1
  3. pop from last stack to output

If we have numbers of 1 to n starting from 1 in the input, what is the minimum value of i which can generate all permutations of 1 to n at the output?

The options are:

  1. 1
  2. 2
  3. n-1
  4. n

Option 1 obviously is not the answer, and also it’s totally possible with n and n-1 stacks witch removes the option 4.

The real question is “is it possible doing it with 2 stacks or we need n-1” ?