In formal language theory, a context-free grammar, G, is said to be in Chomsky normal form (first described by Noam Chomsky)[1] if all of its production rules are of the form:[2][3]
A → BC, or
A → a, or
S → ε,
where A, B, and C are nonterminal symbols, the letter a is a terminal symbol (a symbol that represents a constant value), S is the start symbol, and ε denotes the empty string. Also, neither B nor C may be the start symbol, and the third production rule can only appear if ε is in L(G), the language produced by the context-free grammar G.[4]: 92–93, 106
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one[note 1] which is in Chomsky normal form and has a size no larger than the square of the original grammar's size.
^Chomsky, Noam (1959). "On Certain Formal Properties of Grammars". Information and Control. 2 (2): 137–167. doi:10.1016/S0019-9958(59)90362-6. Here: Sect.6, p.152ff.
^D'Antoni, Loris. "Page 7, Lecture 9: Bottom-up Parsing Algorithms" (PDF). CS536-S21 Intro to Programming Languages and Compilers. University of Wisconsin-Madison. Archived (PDF) from the original on 2021-07-19.
^Sipser, Michael (2006). Introduction to the theory of computation (2nd ed.). Boston: Thomson Course Technology. Definition 2.8. ISBN 0-534-95097-3. OCLC 58544333.
^Hopcroft, John E.; Ullman, Jeffrey D. (1979). Introduction to Automata Theory, Languages and Computation. Reading, Massachusetts: Addison-Wesley Publishing. ISBN 978-0-201-02988-8.
Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).
and 20 Related for: Chomsky normal form information
grammar, G, is said to be in Chomskynormalform (first described by Noam Chomsky) if all of its production rules are of the form: A → BC, or A → a, or...
halt at depth n. Backus–Naur formChomskynormalform Kuroda normalform Greibach, Sheila (January 1965). "A New Normal-Form Theorem for Context-Free Phrase...
The Chomsky hierarchy (infrequently referred to as the Chomsky–Schützenberger hierarchy) in the fields of formal language theory, computer science, and...
standard version of CYK operates only on context-free grammars given in Chomskynormalform (CNF). However any context-free grammar may be algorithmically transformed...
International Airport, Brazil, IATA code CNF Chomskynormalform, in formal language theory, first described by Noam Chomsky Configuration file, in computing, typically...
been made to determine how an infant learns a "non-normal grammar" as theorized by Chomskynormalform. Philosophy portal Artificial intelligence in fiction...
Noam Chomsky, in his 1959 seminal article, used the term "regular" in a different meaning at first (referring to what is called "Chomskynormalform" today)...
Avram Noam Chomsky (born December 7, 1928) is an American professor and public intellectual known for his work in linguistics, political activism, and...
algorithm: an O(n3) algorithm for parsing context-free grammars in Chomskynormalform Earley parser: another O(n3) algorithm for parsing any context-free...
algorithm: an O(n3) algorithm for parsing context-free grammars in Chomskynormalform Earley parser: another O(n3) algorithm for parsing any context-free...
minimum-effort form is known as unmarked; the other, secondary one is marked. In other words, markedness involves the characterization of a "normal" linguistic...
canonical system is said to be in normalform if it has only one initial word and every production rule is of the simple form g $ → $ h {\displaystyle...
biological component of the language faculty, usually credited to Noam Chomsky. The basic postulate of UG is that there are innate constraints on what...
although the method was described before him by Albert Sechehaye in 1908. Chomsky adopted the concept of transformation from his teacher Zellig Harris, who...
all rules is called a growing context-sensitive grammar. Chomsky (1959) introduced the Chomsky hierarchy, in which context-sensitive grammars occur as...
Chomsky. Language is thought to have gradually diverged from earlier primate communication systems when early hominins acquired the ability to form a...