when do we say a grammar to be unambiguous with respect to parse tree and derivation tree?
$begingroup$
In normal terminology we say that both the parse and derivation trees are same in meaning so if a grammar derives one string with left derivation as well as right derivation then it is ambiguous , if both left and right derivation correspond to 2 different parse trees.
Now what if I have the left-most derivation tree to be similar to right-most derivation tree ,and they both correspond to 1 parse tree so can I conclude that the grammar is unambiguous ?
formal-languages automata
edited Dec 7 '15 at 14:47
mvw
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
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add a comment |
$begingroup$
In normal terminology we say that both the parse and derivation trees are same in meaning so if a grammar derives one string with left derivation as well as right derivation then it is ambiguous , if both left and right derivation correspond to 2 different parse trees.
Now what if I have the left-most derivation tree to be similar to right-most derivation tree ,and they both correspond to 1 parse tree so can I conclude that the grammar is unambiguous ?
formal-languages automata
edited Dec 7 '15 at 14:47
mvw
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
$endgroup$
add a comment |
$begingroup$
In normal terminology we say that both the parse and derivation trees are same in meaning so if a grammar derives one string with left derivation as well as right derivation then it is ambiguous , if both left and right derivation correspond to 2 different parse trees.
Now what if I have the left-most derivation tree to be similar to right-most derivation tree ,and they both correspond to 1 parse tree so can I conclude that the grammar is unambiguous ?
formal-languages automata
edited Dec 7 '15 at 14:47
mvw
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
$endgroup$
In normal terminology we say that both the parse and derivation trees are same in meaning so if a grammar derives one string with left derivation as well as right derivation then it is ambiguous , if both left and right derivation correspond to 2 different parse trees.
Now what if I have the left-most derivation tree to be similar to right-most derivation tree ,and they both correspond to 1 parse tree so can I conclude that the grammar is unambiguous ?
formal-languages automata
formal-languages automata
edited Dec 7 '15 at 14:47
mvw
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
edited Dec 7 '15 at 14:47
mvw
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
edited Dec 7 '15 at 14:47
mvw
31.5k22252
edited Dec 7 '15 at 14:47
mvw
31.5k22252
edited Dec 7 '15 at 14:47
mvw
31.5k22252
31.5k22252
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
asked Dec 7 '15 at 14:43
Radha GogiaRadha Gogia
1607
1607
add a comment |
add a comment |
1 Answer
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$begingroup$
An unambiguous grammar has same leftmost and rightmost derivation:
Ambiguous Grammars
Definitions:
If a grammar has more than one leftmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$If a grammar has more than one rightmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$The leftmost and rightmost derivations for a sentential form $color{Red}{text{may
differ,}}$ even in an $color{Green}{text{unambiguous}}$ grammar.
Ref@https://www.eecis.udel.edu/~cavazos/cisc471-672/lectures/Lecture-08.pdf
Comment : Here, last point says an unambiguous grammar has same (or may not be) leftmost and rightmost derivation.
On the other hand, if a grammar has more than one parse tree for any string in given language, then grammar said to be ambiguous.
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
An unambiguous grammar has same leftmost and rightmost derivation:
Ambiguous Grammars
Definitions:
If a grammar has more than one leftmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$If a grammar has more than one rightmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$The leftmost and rightmost derivations for a sentential form $color{Red}{text{may
differ,}}$ even in an $color{Green}{text{unambiguous}}$ grammar.
Ref@https://www.eecis.udel.edu/~cavazos/cisc471-672/lectures/Lecture-08.pdf
Comment : Here, last point says an unambiguous grammar has same (or may not be) leftmost and rightmost derivation.
On the other hand, if a grammar has more than one parse tree for any string in given language, then grammar said to be ambiguous.
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
add a comment |
$begingroup$
An unambiguous grammar has same leftmost and rightmost derivation:
Ambiguous Grammars
Definitions:
If a grammar has more than one leftmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$If a grammar has more than one rightmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$The leftmost and rightmost derivations for a sentential form $color{Red}{text{may
differ,}}$ even in an $color{Green}{text{unambiguous}}$ grammar.
Ref@https://www.eecis.udel.edu/~cavazos/cisc471-672/lectures/Lecture-08.pdf
Comment : Here, last point says an unambiguous grammar has same (or may not be) leftmost and rightmost derivation.
On the other hand, if a grammar has more than one parse tree for any string in given language, then grammar said to be ambiguous.
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
add a comment |
$begingroup$
An unambiguous grammar has same leftmost and rightmost derivation:
Ambiguous Grammars
Definitions:
If a grammar has more than one leftmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$If a grammar has more than one rightmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$The leftmost and rightmost derivations for a sentential form $color{Red}{text{may
differ,}}$ even in an $color{Green}{text{unambiguous}}$ grammar.
Ref@https://www.eecis.udel.edu/~cavazos/cisc471-672/lectures/Lecture-08.pdf
Comment : Here, last point says an unambiguous grammar has same (or may not be) leftmost and rightmost derivation.
On the other hand, if a grammar has more than one parse tree for any string in given language, then grammar said to be ambiguous.
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
$endgroup$
An unambiguous grammar has same leftmost and rightmost derivation:
Ambiguous Grammars
Definitions:
If a grammar has more than one leftmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$If a grammar has more than one rightmost derivation for a single
sentential form, the grammar is $color{Blue}{text{ambiguous}.}$The leftmost and rightmost derivations for a sentential form $color{Red}{text{may
differ,}}$ even in an $color{Green}{text{unambiguous}}$ grammar.
Ref@https://www.eecis.udel.edu/~cavazos/cisc471-672/lectures/Lecture-08.pdf
Comment : Here, last point says an unambiguous grammar has same (or may not be) leftmost and rightmost derivation.
On the other hand, if a grammar has more than one parse tree for any string in given language, then grammar said to be ambiguous.
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
edited Jan 22 '16 at 12:39
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
answered Jan 22 '16 at 12:33
Mithlesh UpadhyayMithlesh Upadhyay
2,93282968
2,93282968
add a comment |
add a comment |
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