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The Chomsky-Schützenberger Hierarchy

Each language class on this table is a proper subset of the class above it.

[Type 0] Recursively Enumerable Languages - Turing Machines
The most powerful machine, the Turing Machine is the equivalent of a computer with infinite memory.
[Type 1] Context-Sensitive Languages - Linear Bounded Automata
The Linear Bounded Automaton is like a Turing Machine, but with a finite amount of memory linearly based on the size of the input.
[Type 2] Context-Free Languages - Pushdown Automata
A Pushdown Automaton is a non-deterministic machine with a finite set of states and a limitless stack.
[Type 3] Regular Languages - Deterministic Finite Automata
A Finite Automaton is a machine with a finite number of states that transitions based only its rules and the next input character.