Table 1.

The Chomsky hierarchy.

Grammars	Languages	Accepting automata
Type 0 grammars, phase-structure grammars, unrestricted grammars	Recursively enumerable	Turing machine, non-deterministic Turing machine
Type 1 grammars, context-sensitive grammars	Context-sensitive	Linear-bounded automata (bounded tape-length Turing machine)
Type 2 grammars, context-free grammars	Context-free	1-Stack pushdown automata
Type 3 grammars, regular grammars, left-linear grammars, right-linear grammars	Regular	Deterministic finite automata, non-deterministic finite automata

Languages are generated by grammars. By gradually imposing restrictions on them (Hopcroft et al., 2007), grammars are categorized into an inclusive four level hierarchy, the Chomsky hierarchy. Type-0 are unrestricted grammars and Type-3 the most restricted. Type-1 grammars correspond to Type-1 Languages which are also called Context Sensitive Languages (CSL). Type-2 and Type-3 correspond to Context Free (CFL) and Regular (RL) languages, respectively. Each class of languages in the Chomsky hierarchy has been characterized as the languages generated by a family of grammars and accepted by a type of machine. The relationships developed between generation and recognition are summarized in this table which is adapted from p. 338 of Sudkamp (2006). Type 0 and Type 1 grammars are accepted by Turing machines, hence the horizontal line in the Table that separates them from Types 2 and 3. Reprinted from Dueñas-Díez and Pérez-Mercader (2019a) Copyright (2019) with permission from Cell Press.