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A pushdown automaton can also manipulate the stack, as part of performing a transition. The manipulation can be to push a particular symbol to the top of the stack, or to pop off the top of the stack. The automaton can alternatively ignore the stack, and leave it as it is.
The two are not equivalent for the deterministic pushdown automaton (although they are for the non-deterministic pushdown automaton). The languages accepted by empty stack are those languages that are accepted by final state and are prefix-free: no word in the language is the prefix of another word in the language. [2] [3]
An embedded pushdown automaton or EPDA is a computational model for parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton, but instead of using a plain stack to store symbols, it has a stack of iterated stacks that store symbols, giving TAGs a generative capacity between context-free and context-sensitive grammars ...
Nested words over the alphabet = {,, …,} can be encoded into "ordinary" words over the tagged alphabet ^, in which each symbol a from Σ has three tagged counterparts: the symbol a for encoding a call position in a nested word labelled with a, the symbol a for encoding a return position labelled with a, and finally the symbol a itself for representing an internal position labelled with a.
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