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In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below).
Nondeterministic finite automaton with ε-moves (NFA-ε) is a further generalization to NFA. In this kind of automaton, the transition function is additionally defined on the empty string ε. A transition without consuming an input symbol is called an ε-transition and is represented in state diagrams by an arrow labeled "ε". ε-transitions ...
These languages are exactly all languages that can be recognized by a non-deterministic pushdown automaton. Context-free languages—or rather its subset of deterministic context-free languages —are the theoretical basis for the phrase structure of most programming languages , though their syntax also includes context-sensitive name ...
Non-deterministic pushdown automata recognize exactly the context-free languages. Examples. This section needs additional citations for ... For example, if the string ...
The halting problem for a register machine: a finite-state automaton with no inputs and two counters that can be incremented, decremented, and tested for zero. Universality of a nondeterministic pushdown automaton: determining whether all words are accepted. The problem whether a tag system halts.
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]
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.
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 ...