HANDLING AMBIUOUS GRAMMARAs we have seen various parsing methods in which if all the grammar is

ambiguous then it creates the conflicts and we cannot parse the input string with such ambiguous grammar. But for some languages in which arithmetic expressions are given ambiguous grammar is most compact and more natural specification as compared to equivalent unambiguous grammar. Secondly using ambiguous grammar we can add any new productions for special constructs. While using ambiguous grammar for input string we will be generated for that specific input. Thus ambiguous grammar can be used in controlled manner for parsing the input. We will consider some ambiguous grammar and let us try to parse some input string.Using precedence and associatively to resolve parsing action conflicts consider an ambiguous grammar for arithmetic expression-E->E+EE->E*EE->(E)E->idNow we will build the set of LR (0)items for this grammar is

Here FOLLOW (E)= {+,*,),$}We have computed FOLLOW (E) as it will be required while processing. Now using the same rules of building SLR (0) parsing table we will generate the parsing table for above set of items.

State Action

goto

id + * ( ) $ E0 s3 s2 1

1 s4 s5accep

t2 s3 s2 63 r4 r4 r44 s3 s2 75 s3 s2 86 s4 s5 s9

7s4 or

r1s5or r1

r1 r1

8s4 or

r2s5 or

r2r2 r2

9 r3 r3 r3

The parse table shift/reduce conflicts occur at state 7 and 8

Stack Input Action with conflict resolution

$0 id+id*id$ Shift

$0id3 +id*id$ Reduce by E→id

$0E1 +id*id$ Shift

$0E1+4 id*id$ Shift

$0E1+4id3 *id$ Reduce by E→id

$0E1+4E7 *id$ The conflict can be resolved by shift 5

$0E1+4E7*5 id$ Shift

$0E1+4E7*5id3 $ Reduce by E→id

$0E1+4E7*5E8 $ Reduce by E→E*E

$0E1+4E7 $ Reduce by E→E+E

$0E1 $ Accept

As * has precedence over + we have to perform multiplication operation first. And that is necessary to push * on the top of the stack. By this we can perform E*E first and then E+E then the parse table is

Stack input Action with conflict resolution

$0 id*id+id$ Shift

$0id3 *id*id$ Reduce by E→id

$0E1 +id*id$ Shift

$0E1*5 id+id$ Shift

$0E1*5id3 +id$ Reduce by E→id

$0E1*5E8 +id$The conflict can be resolved by

reduce by E →E*E

$0E1 +id$ Shift

$0E1+4 id$ Reduce by E→id

$0E1+4id3 $ Reduce by E→E*id

$0E1+4E7 $ Reduce by E→E+E

$0E1 $ Accept