$.(30$ points$)$ For each of the following grammars: $(1)$ construct a CFSM$,(2)$ show the SLR parse table

based on the CFSM and first$/$follow sets, $(3)$ state whether the grammar is SLR or not and explain

why.

$($a$)(10$ points$)$

S $->$ abS $|$ ab

$($b$)(10$ points$)$

S $->$ AaAb $|$ BbBa

A $->$ c

B $->$ c

$($c$)(10$ points$)$

S $->$ ASB $|$ ab

A $->$ a

B $->$ b