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S  S+T|T ; TT*a | a

Nondeterministic Bottom-Up PDA. (q 0 , a + a*a , Z 0 ). S  S+T|T ; TT*a | a. S => S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a. Nondeterministic Bottom-Up PDA. (q 0 , a + a*a , Z 0 ) Ⱶ (q 0 , + a*a , aZ 0 ). S  S+T|T ; TT*a | a.

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S  S+T|T ; TT*a | a

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  1. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  2. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , + a*a , aZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  3. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , + a*a , TZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  4. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  5. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  6. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , *a , a+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  7. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  8. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  9. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  10. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  11. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  12. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  13. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) Ⱶ (q1,1, ᴧ , +SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  14. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) Ⱶ (q1,1, ᴧ , +SZ0) Ⱶ (q1,2, ᴧ , SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  15. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) Ⱶ (q1,1, ᴧ , +SZ0) Ⱶ (q1,2, ᴧ , SZ0) Ⱶ (q0, ᴧ, SZ0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  16. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) Ⱶ (q1,1, ᴧ , +SZ0) Ⱶ (q1,2, ᴧ , SZ0) Ⱶ (q0, ᴧ, SZ0) Ⱶ (q1, ᴧ, Z0) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

  17. Nondeterministic Bottom-Up PDA (q0 , a + a*a , Z0) Ⱶ (q0 , ᴧ+ a*a , aZ0) Ⱶ (q0 , ᴧ+ a*a , TZ0) Ⱶ (q0 , + a*a , SZ0) Ⱶ (q0 , a*a , +SZ0) Ⱶ (q0 , ᴧ*a , a+SZ0) Ⱶ (q0 , *a , T+SZ0) Ⱶ (q0 , a , *T+SZ0) Ⱶ (q0 , ᴧ, a*T+SZ0) Ⱶ (q3,1, ᴧ, *T+SZ0) Ⱶ (q3,2, ᴧ , T+SZ0) Ⱶ (q0, ᴧ, T+SZ0) Ⱶ (q1,1, ᴧ , +SZ0) Ⱶ (q1,2, ᴧ , SZ0) Ⱶ (q0, ᴧ, SZ0) Ⱶ (q1, ᴧ, Z0) Ⱶ (q2, ᴧ , ᴧ) S  S+T|T ; TT*a | a S=>S+T=>S+T*a=>S + a*a=>T + a*a=>a + a*a

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