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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.
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.
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 ...
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]
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.
Parsing: Finding a valid derivation using an automaton. Parse Tree: The alignment of the grammar to a sequence. An example of a parser for PCFG grammars is the pushdown automaton. The algorithm parses grammar nonterminals from left to right in a stack-like manner. This brute-force approach is not very efficient.
A TAG can describe the language of squares (in which some arbitrary string is repeated), and the language {|}. This type of processing can be represented by an embedded pushdown automaton. Languages with cubes (i.e. triplicated strings) or with more than four distinct character strings of equal length cannot be generated by tree-adjoining grammars.
The notion of the DCFL is closely related to the deterministic pushdown automaton (DPDA). It is where the language power of pushdown automata is reduced to if we make them deterministic; the pushdown automata become unable to choose between different state-transition alternatives and as a consequence cannot recognize all context-free languages. [1]