The context free grammar: (e represents epsilon)
S --> aSb|aSa|bSa|bSb|e
It could generate regular language which means it can be converted to a right linear grammar. Is there a general rule to convert CFG into a RLG?
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So in this case, your desired output would be `S --> aaS|abS|baS|bbS|e`? – ruakh Feb 07 '13 at 01:03
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This question might be better fit for http://programmers.stackexchange.com or http://cs.stackexchange.com – Andrew Savinykh Feb 07 '13 at 02:23
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There is no general algorithm for converting a CFG to a right-linear grammar because right-linear grammars generate precisely the regular languages, which are a strict subset of the context-free languages. Accordingly, if a general algorithm existed that performed this transformation, it would prove all context-free languages are regular, which is known to be false.
Hope this helps!
templatetypedef
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If there is no general rule to do that, could you show me how to convert the CFG above into a RLG? – henry Feb 07 '13 at 13:54
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@henry- If you look at the above grammar, you'll note that it generates all even-length strings made from a's and b's. Given that insight, you can try creating, from scratch, a right linear grammar that generates the same language. – templatetypedef Feb 07 '13 at 18:46