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Consider the ...

Question

$C o n s i d e r t h e f o l l o w i n g p r o b l e m s o n d e c i d a b i l i t y : 1 . G i v e n a C F G G a n d a s t r i n g ω \in \sum * . d o e s ω b e l o n g s t o L (G) ? 2 . G i v e n a T u n i n g M a c h i n e T, a s t r i n g ω \in \sum * a n d a n i n t e g e r K, d o e s T a c c e p t ω w i t h i n k s t e p s ? 3 . G i v e n a T u n i n g M a c h i n e T, a s t r i n g ω \in \sum * a n d a s t a t e q \in Q (s e t o f s t a t e o f t h e T u n i n g M a c h i n e) . d o e s t h e c o m p u t a t i o n o f T o n ω v i s i t t h e s t a t e q ? T h e t o t a l n u m b e r o f d e i d a b l e p r o b l e m s a r e______.$

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Solution

$1 i s t h e m e m b e r s h i p p r o b l e m f o r C F L s, f o r w h i c h w e h a v e t h e C Y K a l g o r i t h m, T h e r e f o r e d e c i d a b l e . 2 i s d e c i d a b l e b e c a u s e w e c a n s i m u l a t e t h e T u n i n g M a c h i n e T o n ω f o r k s t e p s a n d c h e c k w h e t h e r T c o m e s t o a h a l t o r n o t . T h e r e f o r e 2 i s d e c i d a b l e . 3 i s t h e w e l l k n o w n s t a t e e n t r y p r o b l e m, w h i c h i s u n d e c i d a b l e .$

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Similar questions

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P_{1}

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