Closure properties of regular languages

36 45§ 4*¢¦)©2$§£% /-¦0/¨.$"¤"¦1$§ ++££§ £)£ ¨ )¨¨¨ *§ ¦*¨.¨ ¦¤$¢¢¤¤££5 6 43* § 4©) ¦¨+¨+¥¥¨¨ExamplesProve the following languages to be non-regular:For anyIN, take%, then pump.For anyIN, takein the splitis prime 7 " 87 ¨for a prime£. Then pump tois not prime.such that+.02140 Languages and Parsing, MF, Fall 2004 – p.7/8Closure properties of regular languagesThe regular languages are closed underunion — i.e., the union of two regular languages is regular,intersection — i.e., the intersection of two reg. lang.s is regular,complement — i.e., the complement of a reg. lang. is regular,difference — i.e., the difference of two reg. lang.s is regular,reversal — i.e., the language containing the reversals of thewords of a reg. lang. is regular,closure (Kleene star) — i.e., the closure of a reg. lang. is regular,concatenation — i.e., the catenation of two reg. lang.s is regular,homomorphism — i.e., the image of a reg. lang. under ahomomorphism is regular,inverse homomorphism — i.e., the pre-image of a reg. lang.under a homomorphism is regular.02140 Languages and Parsing, MF, Fall 2004 – p.8/8