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Explain closure properties of CFL

Mumbai university > Comp > SEM 4 > TCS

Marks: 5M

Year: May 2014

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  1. Context-free languages are closed under Union

    If $L_1$ is context-free and $L_2$ is context-free, then $L_1 \ U \ L_2$

  2. Context-free languages are closed under Concatenation If $L_1$ is context-free and $L_2$ is context-free, then $L_1L_2$

  3. Context-free languages are closed under Star operation If L is context-free, then L*

Negative properties:

  1. Context-free languages are not closed under Intersection If $L_1$ is context-free and $L_2$ is not necessarily context-free, then $L_1 \ ∩ \ L_2$

  2. Context-free languages are not closed under Complement If $L_1$ is context-free, then $L_1$ complement is not necessarily context-free

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