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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]
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]
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 ...
Thus the language = {} cannot be accepted by a visibly pushdown automaton for any partition of , however there are pushdown automata accepting this language. If a language L {\displaystyle L} over a tagged alphabet Σ ^ {\displaystyle {\hat {\Sigma }}} is accepted by a deterministic visibly pushdown automaton, then L {\displaystyle L} is called ...
Every grammar in Kuroda normal form is noncontracting, and therefore, generates a context-sensitive language. Conversely, every noncontracting grammar that does not generate the empty string can be converted to Kuroda normal form. [2]