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In automata theory, a deterministic pushdown automaton (DPDA or DPA) is a variation of the pushdown automaton. The class of deterministic pushdown automata accepts the deterministic context-free languages, a proper subset of context-free languages. [1]
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 pushdown automaton (DPDA) deterministic context-free languages: Pushdown automaton (PDA) context-free languages: Linear bounded automaton (LBA) context-sensitive languages: Turing machine: recursively enumerable languages: Deterministic Büchi automaton: ω-limit languages: Nondeterministic Büchi automaton ω-regular languages
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]
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.
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Deterministic context-free grammars are accepted by deterministic pushdown automata and can be parsed in linear time, for example by an LR parser. [7] They are a strict subset of the context-free grammars, which are accepted by pushdown automata and can be parsed in polynomial time, for example by the CYK algorithm.