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A pushdown automaton reads a given input string from left to right. In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition.
This conversion can be used to prove that every context-free language can be accepted by a real-time (non-deterministic) pushdown automaton, i.e., the automaton reads a letter from its input every step. Given a grammar in GNF and a derivable string in the grammar with length n, any top-down parser will halt at depth n.
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]
JFLAP (Java Formal Languages and Automata Package) is interactive educational software written in Java for experimenting with topics in the computer science area of formal languages and automata theory, primarily intended for use at the undergraduate level or as an advanced topic for high school.
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.
A derivation of a string for a grammar is a sequence of grammar rule applications that transform the start symbol into the string. A derivation proves that the string belongs to the grammar's language. A derivation is fully determined by giving, for each step: the rule applied in that step; the occurrence of its left-hand side to which it is ...
Deterministic context-free grammars were particularly useful because they could be parsed sequentially by a deterministic pushdown automaton, which was a requirement due to computer memory constraints. [4] In 1965, Donald Knuth invented the LR(k) parser and proved that there exists an LR(k) grammar for every deterministic context-free language. [5]