Chomsky Normal Form

Ramos MVM, de Queiroz RJGB, Moreira N, Almeida JB.  2016.  On the Formalization of Some Results of Context-Free Language Theory. Logic, Language, Information, and Computation – 23rd International Workshop, WoLLIC 2016. 9803 Abstract16wollic.pdf

This work describes a formalization effort, using the Coq proof assistant, of fundamental results related to the classical theory of context-free grammars and languages. These include closure properties (union, concatenation and Kleene star), grammar simplification (elimi- nation of useless symbols, inaccessible symbols, empty rules and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. This is probably the most comprehensive formalization of the classical context-free language theory in the Coq proof assistant done to the present date, and includes the important result that is the formalization of the Pumping Lemma for context-free languages.