On left recursive context-free grammars
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Definition Context-free grammar $G$ is said to be left-recursive, if there exists such non-terminal symbol $A$, that one can derive from it a word $Aalpha$, where $alpha$ is a word over unified terminal and non-terminal alphabets.
Given $G$ with terminal alphabet ${a, b, c}$, non-terminal alphabet ${S, R, T}$ and rules:
$ S to aR$
$ R to bRT | varepsilon$
$ T to cSR | varepsilon$
am I right in assuming $G$ is not left recursive, as any word derivable from any non-terminal is either empty or starts with a terminal symbol?
formal-languages context-free-grammar
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
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add a comment |
$begingroup$
Definition Context-free grammar $G$ is said to be left-recursive, if there exists such non-terminal symbol $A$, that one can derive from it a word $Aalpha$, where $alpha$ is a word over unified terminal and non-terminal alphabets.
Given $G$ with terminal alphabet ${a, b, c}$, non-terminal alphabet ${S, R, T}$ and rules:
$ S to aR$
$ R to bRT | varepsilon$
$ T to cSR | varepsilon$
am I right in assuming $G$ is not left recursive, as any word derivable from any non-terminal is either empty or starts with a terminal symbol?
formal-languages context-free-grammar
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
$endgroup$
$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
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– Ronald
Dec 7 '18 at 13:10
1
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@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25
add a comment |
$begingroup$
Definition Context-free grammar $G$ is said to be left-recursive, if there exists such non-terminal symbol $A$, that one can derive from it a word $Aalpha$, where $alpha$ is a word over unified terminal and non-terminal alphabets.
Given $G$ with terminal alphabet ${a, b, c}$, non-terminal alphabet ${S, R, T}$ and rules:
$ S to aR$
$ R to bRT | varepsilon$
$ T to cSR | varepsilon$
am I right in assuming $G$ is not left recursive, as any word derivable from any non-terminal is either empty or starts with a terminal symbol?
formal-languages context-free-grammar
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
$endgroup$
Definition Context-free grammar $G$ is said to be left-recursive, if there exists such non-terminal symbol $A$, that one can derive from it a word $Aalpha$, where $alpha$ is a word over unified terminal and non-terminal alphabets.
Given $G$ with terminal alphabet ${a, b, c}$, non-terminal alphabet ${S, R, T}$ and rules:
$ S to aR$
$ R to bRT | varepsilon$
$ T to cSR | varepsilon$
am I right in assuming $G$ is not left recursive, as any word derivable from any non-terminal is either empty or starts with a terminal symbol?
formal-languages context-free-grammar
formal-languages context-free-grammar
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
asked Dec 7 '18 at 11:25
DrinkwaterDrinkwater
538210
538210
$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
$endgroup$
– Ronald
Dec 7 '18 at 13:10
1
$begingroup$
@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25
add a comment |
$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
$endgroup$
– Ronald
Dec 7 '18 at 13:10
1
$begingroup$
@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25
$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
$endgroup$
– Ronald
Dec 7 '18 at 13:10
$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
$endgroup$
– Ronald
Dec 7 '18 at 13:10
1
1
$begingroup$
@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25
$begingroup$
@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25
add a comment |
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Yes, you are correct. Any sentence derivable from any non-terminal starts with a terminal, except for the empty sentence. So there is no left-recursion.
answered Dec 7 '18 at 16:24
ricirici
37829
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$begingroup$
Yes, you are correct. Any sentence derivable from any non-terminal starts with a terminal, except for the empty sentence. So there is no left-recursion.
answered Dec 7 '18 at 16:24
ricirici
37829
$endgroup$
add a comment |
$begingroup$
Yes, you are correct. Any sentence derivable from any non-terminal starts with a terminal, except for the empty sentence. So there is no left-recursion.
answered Dec 7 '18 at 16:24
ricirici
37829
$endgroup$
add a comment |
$begingroup$
Yes, you are correct. Any sentence derivable from any non-terminal starts with a terminal, except for the empty sentence. So there is no left-recursion.
answered Dec 7 '18 at 16:24
ricirici
37829
$endgroup$
Yes, you are correct. Any sentence derivable from any non-terminal starts with a terminal, except for the empty sentence. So there is no left-recursion.
answered Dec 7 '18 at 16:24
ricirici
37829
answered Dec 7 '18 at 16:24
ricirici
37829
answered Dec 7 '18 at 16:24
ricirici
37829
answered Dec 7 '18 at 16:24
ricirici
37829
37829
add a comment |
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$begingroup$
if I read the wikipedia article on left-recursion correctly (en.wikipedia.org/wiki/Left_recursion), your grammar looks like the indirect left recursive grammar.
$endgroup$
– Ronald
Dec 7 '18 at 13:10
1
$begingroup$
@Ronald: it's only indirect left recursion if you can derive $Aalpha$ from $A$ for some $A$. (As OP says.) In this case, you cannot.
$endgroup$
– rici
Dec 7 '18 at 16:25