Theorem 3.1 The complement of any regular language is a regular language. Let L be any regular language.
{"Image DocumentName": "Theorem 3.1The complement of any regular language is a regular language. Let L be any regular language.", "Image ImageDescription": "By definition there must be some DFA M = (Q, \uf053, \uf064, q0, F) with L(M) = L. Define a new DFA M = (Q, \uf053, \uf064, q0, Q-F) This has the same transition function \uf064 as M, but for any string x \uf0ce \uf053  it accepts x if and only if M rejects x. Thus L(M ) is the complement of L. Because there is a DFA for it, we conclude that the complement of L is regular. Formal Language, chapter 3, slide 7.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}