# Paths with DFA?

My teacher made an example to explain DFA, it was about paths (URL paths), the rules were as follows:

S ::= /
S ::= /O
O ::= [a-z]
O ::= [a-z]R
O ::= [a-z]S
R ::= [a-z]
R ::= [a-z]R
R ::= [a-z]S


Examples of paths could be: /foo, /foo/, foo/bar and so on.

However, I don't understand why you would need the R rules since they are equal to the O rules.

Can I write it without the R? If not, why?

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By DFA, do you mean Deterministic Finite Automata or something else? –  Chris Taylor Jun 9 '11 at 21:51
I guess it is en.wikipedia.org/wiki/Deterministic_finite-state_machine. However, the way of actually displaying it may be unorthodox in my case. –  whirlwin Jun 9 '11 at 21:57

You don't need them, in fact. The grammar you wrote is equivalent to the one obtained by deleting the R rules and substituting the second O rule by
O ::= [a-z]O