How can I eliminate left recursion in the following grammar?

问题

Here's the grammar, which is supposed to describe a language of nested braces with commas as delimiters:

L ::= {L} | L,L |

A few more examples of strings I'd expect the grammar to accept and reject:

Accept:

{,{,,{,}},,{,}}
{{{{}}}}
{,{}}

Reject:

{}{}
{,{}{}}
{{},{}

回答1:

Done by hand:

L ::= { L } | { L } , | , L | ε

Or, instead of just winging it we could use a more systematic approach and apply the algorithm from Wikipedia on removing immediate left recursion:

L ::= { L } L₁ | L₁
L₁ ::= ε | , L L₁

回答2:

First of all, that grammar won't accept your first example, since it requires the commas to be after the close brace and before the open brace. I would suggest to re-write it as

L::= {L} | ,L

This won't get rid of the left recursion, but it will at least match your acceptable answers.

来源：https://stackoverflow.com/questions/1095774/how-can-i-eliminate-left-recursion-in-the-following-grammar