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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 .
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]
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 ...
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.
Nowhere in the page is the concept of deterministic context-free language defined. Supposedly a DCFL is one accepted by a DPDA, but there are two different acceptance criteria, and you never mention which one is used. Can you provide a complete definition of "the language accepted by a DPDA"? Yuval Filmus 21:44, 16 September 2016 (UTC)
A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value ...