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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).
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.
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 ...
The obtained automaton is non-deterministic, and it has as many states as the number of letters of the regular expression, plus one. Furthermore, it has been shown [ 3 ] : 215 [ 4 ] that Glushkov's automaton is the same as Thompson's automaton when the ε-transitions are removed.
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 ...
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.
Non-deterministic pushdown automata are another formalism equivalent to context-free grammars. Different models of computation have the ability to do different tasks. One way to measure the power of a computational model is to study the class of formal languages that the model can generate; in such a way the Chomsky hierarchy of languages is ...
Deterministic: For a given current state and an input symbol, if an automaton can only jump to one and only one state then it is a deterministic automaton. Nondeterministic : An automaton that, after reading an input symbol, may jump into any of a number of states, as licensed by its transition relation.