Arrange in the increasing order of power of following automata-

Question

Realtime DPDA with Null Store,Real time DPDA with final state, DPDA with NULL store,DPDA with final state, NPDA

Answer 1

Simply consider Realtime DPDA means DPDA which doesn’t have epsilon moves! Hence we cannot push or pop without having any symbol. 

Hence it is less powerful than normalDPDA.

and acceptance by empty stack in DPDA(either realtime or normal) sometimes doesn’t follows prefix property hence it is less powerful than final state acceptance. 

Hence order is

Realtime DPDA with Empty state < RT DPDA with final state < DPDA with empty state < DPDA with final state < NPDA

Answer 2

real time DPDA with null<real time DPDA WITH FINAL<DPDA with NULl<DPDA with final<NPDA

Comments

Could you please give me example of a language for the first two? I can think of any example on my own.

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what is this "real time DPDA"?

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I guess every DPDA has the same power and NPDA has greater or equal power than DPDA. Can you kindly provide the source from where you found this answer?

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A context-free language is said to be real-time strict if it is accepted by a real-time deterministic pushdown automaton with empty stack acceptance.

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@ Rishabh Jain 1

every DPDA donot have same power acceptance by empty stack and final state both have different power

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please explain it with reason is it due to prefix property?