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The PDA accepts by empty stack. Its initial stack symbol is the grammar's start symbol. [3] For a context-free grammar in Greibach normal form, defining (1,γ) ∈ δ(1,a,A) for each grammar rule A → aγ also yields an equivalent nondeterministic pushdown automaton. [4] The converse, finding a grammar for a given PDA, is not that easy.
For example, the language L p of even-length palindromes on the alphabet of 0 and 1 has the context-free grammar S → 0S0 | 1S1 | ε. If a DPDA for this language exists, and it sees a string 0 n , it must use its stack to memorize the length n , in order to be able to distinguish its possible continuations 0 n 11 0 n ∈ L p and 0 n 11 0 n +2 ...
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.
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] This parser still required a lot of memory. In 1969 Frank DeRemer invented the LALR and Simple LR parsers, both based on the LR parser and having greatly reduced memory requirements at the cost of less ...
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.
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language.
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