I came across following fact in Automata book by Hopcroft, Ullman:

> For every PDA accepting by empty stack (PDAeS), there is an equivalent one state PDA accepting by empty stack.

I was wondering how this applies to:

1. PDA accepting by final state (PDAfS)
2. Deterministic PDA accepting by empty stack (DPDAeS)
3. Deterministic PDA accepting by final state (DPDAfS)

My understanding is, it applies equally to PDAfS, since I read in the book that both PDAfS and PDAeS are of equal power. Am I right? Also what about DPDAs?

Also I came across [this](https://cs.stackexchange.com/questions/21494/are-all-pda-equivalent-to-two-state-pda) post, which states:

> All PDAs are equivalent to two state PDAs.

I want to know what all variants (PDAfS, PDAeS, DPDAeS, DPDAfS) it refers to by PDA? Reading the explanation given in the problem itself, my guess is that it is possible with PDAeS and DPDeS. Am I right?