问题描述
无上下文语言集合的联合是否总是无上下文关系？证明您的答案是正确的....
Is the union of a collection of context-free languages always context-free ? Justify your answer .....
我知道答案是肯定的，但是我怎么证明呢？
I know that the answer is yes, but how can I prove it ?
推荐答案
要显示上下文无关语言的有限联合是上下文无关的，您只需要构建上下文无关的语法对于联合语言，就像您要证明两种无上下文语言的联合是无上下文的一样。
To show that the finite union of context-free languages is context-free you just have to build a context-free grammar for the union language, exactly as you would do to prove that the union of two context-free languages is context-free.
如果G1，...，GN是您拥有的N种无上下文语言的无上下文语法，请重命名每个语法中的所有符号（添加一个下标只是为了避免符号名称冲突），然后使用N个语法的所有乘积加上乘积来制作新的语法G：
If G1,...,GN are the context-free grammars for the N context-free languages you have, rename all the symbols in the each grammar (add a subscript just to avoid symbol name clashes) and then make a new grammar G with all the productions from the N grammars, plus the production:
S-> S1 | S2 | ... | SN
S -> S1 | S2 | ... | SN
此语法生成联合语言，并且没有上下文。
This grammar generates the union language, and it is context-free.
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