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It can only choose a new state, the result of following the transition. A pushdown automaton (PDA) differs from a finite state machine in two ways: It can use the top of the stack to decide which transition to take. It can manipulate the stack as part of performing a transition. A pushdown automaton reads a given input string from left to right.
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]
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.
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.
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 ...
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In the classic formalization of generative grammars first proposed by Noam Chomsky in the 1950s, [2] [3] a grammar G consists of the following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules, each rule of the form