$W e d e f i n e t h e p o w e r s o f a s t r i n g ω o v e r t h e c o n c a t e n a t i o n o p e r a t i o n () a s f o l l o w s : ω^{0} = \in ω^{i + 1} = ω^{i} . ω (1^{3} + 1^{2019}) + (1^{6} + 1^{2016}) * T h e n u m b e r o f s t a t e s i n t h e m i n i m a l D F A (o v e r t h e u n a r y a l p h a b e t (1}) o f t h e l a n g u a g e c o r r e s p o n d i n g t o t h e r e g u l a r e x p r e s s i o n i s e q u a l t o______.$

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Solution

$T h e r e g u l a r e x p r e s s i o n i s (1^{3} + 1^{2019}) * + (1^{6} + 1^{2016}) * W h i c h i s s a m e a s, (1^{3}) * + (1^{6}) * = (111) * + (111111) * = (111) * (a s (111) * i s a s u p e r s e t o f (111111) *] W h i c h o n l y r e q u i r e s 3 s t a t e s .$

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