Chomsky hierarchy

Automata theory: formal languages and formal grammars

Chomsky hierarchy describes the relations between various languages and kinds of formalized logic.

  • | (no common name) | Decidable | Decider Ty-1| Context-sensitive | Context-sensitive | Linear-bounded

  • | Positive range concat| Positive range concat | PTIME TM

  • | Indexed | Indexed | Nested stack

  • | - | - | Thread automaton

  • | Linear CF rewrite sys| Linear CF rewrite lang| Restricted treestack aut

  • | Tree-adjoining | Tree-adjoining | Embedded PDA Ty-2| Context-free (CF) | Context-free | Nondeterministic PDA

  • | Deterministic CF | Deterministic CF | Deterministic PDA

  • | Visibly PDA | Visibly PDA | Visibly PDA Ty-3| Regular | Regular | Finite

  • | - | Star-free | Counter-free

  • | Non-recursive | Finite | Acyclic finite

Each category of languages, except those marked by an asterisk, is a proper subset of the category directly above it.

Any language in each category is generated by a grammar and by an automaton in the category in the same line.

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