Nested stack automaton
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In automata theory, a nested stack automaton is a finite automaton that can make use of a stack containing data which can be additional stacks.[1] A nested stack automaton may read its stack, in addition to pushing or popping it. A nested stack automaton is capable of recognizing an indexed language.[2]
[edit] See also
[edit] References
- ^ Aho, Alfred (1969). "Nested stack automata". Journal of the ACM 16 (3): 383β406. doi:. ISSN 0004-5411.
- ^ Partee, Barbara; Alice ter Meulen, and Robert E. Wall (1990). Mathematical Methods in Linguistics. Kluwer Academic Publishers, 536β542. ISBN 978-90-277-2245-4.
| Chomsky hierarchy |
Grammars | Languages | Minimal automaton |
|---|---|---|---|
| Type-0 | Unrestricted | Recursively enumerable | Turing machine |
| n/a | (no common name) | Recursive | Decider |
| Type-1 | Context-sensitive | Context-sensitive | Linear-bounded |
| n/a | Indexed | Indexed | Nested stack |
| n/a | Tree-adjoining etc. | (Mildly context-sensitive) | Embedded pushdown |
| Type-2 | Context-free | Context-free | Nondeterministic pushdown |
| n/a | Deterministic context-free | Deterministic context-free | Deterministic pushdown |
| Type-3 | Regular | Regular | Finite |
| n/a | Star-free | Counter-Free | |
| Each category of languages or grammars is a proper subset of the category directly above it, and any automaton in each category has an equivalent automaton in the category directly above it. |
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