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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]
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.
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
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 ...
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 ...