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Regular version of the site

Article

Bar-Hillel Theorem Mechanization in Coq

Lecture Notes in Computer Science. 2019. Vol. 11541. P. 264-281.
Grigorev S., Bozhko S., Хатбуллина Л. Р.

Formal language theory has a deep connection with such areas as static code analysis, graph database querying, formal verifica- tion, and compressed data processing. Many application problems can be formulated in terms of languages intersection. The Bar-Hillel theo- rem states that context-free languages are closed under intersection with a regular set. This theorem has a constructive proof and thus provides a formal justification of correctness of the algorithms for applications mentioned above. Mechanization of the Bar-Hillel theorem, therefore, is both a fundamental result of formal language theory and a basis for the certified implementation of the algorithms for applications. In this work, we present the mechanized proof of the Bar-Hillel theorem in Coq.