Difference between revisions of "Grammar: Decidable and Undecidable Problems"

(Created page with ":{| class="wikitable" |+ align="top"|Closure properties of language families |- ! Operation ! Regular ! DCFL ! CFL ! CSL ! Recursive ! RE |- |Union | {{Yes}} | {{No}} | {{Yes}...")
 
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|+ align="top"|Closure properties of language families
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|+ align="top"|Grammar: Decidable and Undecidable Problems
 
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|-
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! Operation
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! Grammar
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! Regular
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! <math>w \in L(M)</math>
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! DCFL
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! <math>L(M) = \phi</math>
−
! CFL
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! <math>L = \Sigma^*</math>
−
! CSL
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! <math>L(M_1) \subseteq L(M_2)</math>
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! Recursive
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! <math>L(M_1) = L(M_2)</math>
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! RE
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! <math>L(M_1) \cap L(M_2) = \phi</math>
 
|-
 
|-
 
|Union
 
|Union

Revision as of 17:59, 26 February 2014

Grammar: Decidable and Undecidable Problems
Grammar <math>w \in L(M)</math> <math>L(M) = \phi</math> <math>L = \Sigma^*</math> <math>L(M_1) \subseteq L(M_2)</math> <math>L(M_1) = L(M_2)</math> <math>L(M_1) \cap L(M_2) = \phi</math>
Union Yes No Yes Yes Yes Yes
Intersection Yes No No Yes Yes Yes
Complement Yes Yes No Yes Yes No
Concatenation Yes No Yes Yes Yes Yes
Kleene star Yes No Yes Yes Yes Yes
Homomorphism Yes No Yes No No Yes
<math>\epsilon</math>-free Homomorphism Yes No Yes Yes Yes Yes
Substitution (<math>\epsilon</math>-free) Yes No Yes Yes No Yes
Inverse Homomorphism Yes Yes Yes Yes Yes Yes
Reverse Yes No Yes Yes Yes Yes
Retrieved from "https://gatecse.in/w/index.php?title=Grammar:_Decidable_and_Undecidable_Problems&oldid=2640"
Closure properties of language families
Operation Regular DCFL CFL CSL Recursive RE
Union Yes No Yes Yes Yes Yes
Intersection Yes No No Yes Yes Yes
Complement Yes Yes No Yes Yes No
Concatenation Yes No Yes Yes Yes Yes
Kleene star Yes No Yes Yes Yes Yes
Homomorphism Yes No Yes No No Yes
<math>\epsilon</math>-free Homomorphism Yes No Yes Yes Yes Yes
Substitution (<math>\epsilon</math>-free) Yes No Yes Yes No Yes
Inverse Homomorphism Yes Yes Yes Yes Yes Yes
Reverse Yes No Yes Yes Yes Yes