4.6.5
lr(0) items in initial:
s』 -> s
s -> aaab|bbba
a -> e
b ->e
so , i
: s』 ->·s
s ->
·aaab
s ->
·bbba
a ->
·b ->
·follow(a) = follow(b) =
therefore, when input 『a』 we may get a conflict since follow(a) = follow(b).
this grammar is not slr(1)
first(s) =
first(a) = f irst(b) =
follow(s) =
follow(a) = follow(b)=
the parse table isab
$ss -> aaab
s ->bbba
aa -> e
a -> e
bb -> e
b -> e
there are no conflicts , so the grammar is ll(1).
4.6.6
first(s) =
first(a) =
follow(s) =
follow(a) =
the parse table is :a$
ss – sa
s -> a
aa -> a
there is a conflict , so it is not ll(1). theni:
s』 -> ·s
s -> ·sa
s -> ·a
a -> ·a
i:s』 -> ·s
s -> s·a
a -> ·a
i:s -> a·i
:a -> a·i
:s -> sa
·so the parse table is
state
action
goto a
$sa0
s3121
s3acc42
y2r23y3
r34r1r1
there are no conflicts , so the grammar is slr(1).
4.7.1
(a)lri:
s』 ->
·s , $
s ->
·ss+ , $/a
s ->
·ss* , $/a
s ->
·a , $/a i
:s』 -> s
·, $
s -> s
·s+ , $/a
s -> s
·s* , $/a
s ->
·ss+ , +/*/a
s ->
·ss* , +/*/a
s ->
·a , +/*/a i
:s -> a
·, $/+/*/a i
:s ->s s
·, $/a
s -> ss
·+ , $/a
s -> ss
·* , $/a
s -> s
·s+ , +/*/a
s -> s
·s* , +/*/a
s ->
·ss+ , +/*/a
s ->
·ss* , +/*/a
s ->
·a , +/*/a i
:s -> a
·, +/*/a i
:s -> ss
·+ , +/*/a
s -> ss
·* , +/*/a
s -> s
·s+ , +/*/a
s -> s
·s* , +/*/a
s ->
·ss+ , +/*/a
s ->
·ss* , +/*/a
s ->
·a , +/*/a i
:s -> ss+
·, $/a i
:s -> ss*
·, $/a i
:s -> ss+
·, +/*/a i
:s -> ss*
·, +/*/a
(b)lalri:
s』 ->
·s , $
s ->
·ss+ , $/a
s ->
·ss* , $/a
s ->
·a , $/a i
:s』 -> s
·, $
s -> s
·s+ , $/a
s -> s
·s* , $/a
s ->
·ss+ , +/*/a
s ->
·ss* , +/*/a
s ->
·a , +/*/a i
:s -> a
·, $/+/*/a i
:s -> ss
·+ , $/+/*/a
s -> ss
·* , $/+/*/a
s -> s
·s+ , +/*/a
s -> s
·s* , +/*/a
s ->
·ss+ , +/*/a
s ->
·ss* , +/*/a
s ->
·a , +/*/a i
:s -> ss+
·, $/+/*/a i
:s -> ss*
·, $/+/*/a
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