Chomsky hierarchy
Grammar complexity ranking
The Chomsky hierarchy is a classification of formal grammars into four nested types, each generating increasingly complex languages.
Type 3 (regular) grammars are the most restricted; type 2 (context-free) describe most programming languages; type 1 (context-sensitive) and type 0 (unrestricted) allow progressively more computational power.
The hierarchy maps directly onto classes of abstract machines—finite automata, pushdown automata, linear-bounded automata, and Turing machines.
Named for linguist Noam Chomsky, who proposed it in 1956.
Production system, single left nonterminals
- derivationSource or origin tracing
- ambiguityOpenness to multiple interpretations
- recursionProcess invoking itself
Self-moving mechanical devices
- Turing machineMathematical model of computation
- decidabilityAlgorithmic resolution capability
- computabilityAlgorithmic solvability of problems
- context-sensitiveVarying by situation
deterministic · non-deterministic · Church-Turing thesis · acceptance · rejection · tape · alphabet
Heights or ranked stages
- containmentPreventing hostile expansion
- expressivenessAbility to convey emotion
- stratificationDivision into distinct levels
- restrictionLimit on action
power · inclusion · language classes · nesting · subset · superset · computational power
Innate linguistic faculty hypothesis
- natural languageHuman communication, not programming
- language acquisitionDeveloping communication ability
- competenceAdequate ability to function
- innatenessBeing inherent from birth
context-free grammar
Production system, single left nonterminals
- derivationSource or origin tracing
- ambiguityOpenness to multiple interpretations
- recursionProcess invoking itself
automata
Self-moving mechanical devices
- Turing machineMathematical model of computation
- decidabilityAlgorithmic resolution capability
- computabilityAlgorithmic solvability of problems
context-sensitive · deterministic · non-deterministic · Church-Turing thesis · acceptance · rejection · tape · alphabet
levels
Heights or ranked stages
- containmentPreventing hostile expansion
- expressivenessAbility to convey emotion
- stratificationDivision into distinct levels
restriction · power · inclusion · language classes · nesting · subset · superset · computational power
universal grammar
Innate linguistic faculty hypothesis
- natural languageHuman communication, not programming
- language acquisitionDeveloping communication ability
- competenceAdequate ability to function
- Chomskyuniversal grammar, minimalist program, competence, performance, recursion
- Chomsky linguisticsuniversal grammar, merge, move, minimalist program, government
- syntax theoriesuniversal grammar, minimalist program, CCG, context-free grammar, merge
- Algorithm Analysisruntime, running time, growth rate, complexity, linear
- lambda calculuslambda, abstraction, application, bound variable, substitution
- syntax treesbranches, branching, noun phrase, verb phrase, prepositional phrase
Chomsky hierarchynatural language
Human communication, not programming
sociolinguistics · phonology · morphology · phonetics · dialectology
Chomsky hierarchyproduction code
Software serving real users
hierarchy, hierarchical, hierarchies, hierarchically, nonhierarchical, Chomsky