Search results
Results From The WOW.Com Content Network
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]
For each pushdown automaton one may construct a context-free grammar such that () = (). [5] The language of strings accepted by a deterministic pushdown automaton (DPDA) is called a deterministic context-free language. Not all context-free languages are deterministic.
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]
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]
As the definition of visibly pushdown automata shows, deterministic visibly pushdown automata can be seen as a special case of deterministic pushdown automata; thus the set VPL of visibly pushdown languages over ^ forms a subset of the set DCFL of deterministic context-free languages over the set of symbols in ^. In particular, the function ...
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.
The () parser is a deterministic pushdown automaton with the ability to peek on the next input symbols without reading. This peek capability can be emulated by storing the lookahead buffer contents in the finite state space, since both buffer and input alphabet are finite in size.
LR grammars (also known as deterministic context-free grammars) allow parsing (string recognition) with deterministic pushdown automata (PDA), but they can only describe deterministic context-free languages. Simple LR, Look-Ahead LR grammars are subclasses that allow further simplification of parsing. SLR and LALR are recognized using the same ...