Question

(20 pts) Create an LR(O) parse table for the following grammar. Show all steps (creating closures, the DFA, the transition table, and finally the parse table): E->E+T E*T T T->(E) | id Show a complete bottom-up parse, including the parse stack contents, input string, and action for the string below using the parse table you created (id + id) * id Show a rightmost derivation for the string above, and show how the bottom-up parse you completed correctly finds all of the handles for the input string above.

Answer 1

for the given Grommer Terminals are = ( id ), + ,* } Non-Terminals are = E,ETY Start symbol = {E1} Production E EIT 2 E EXT ③ ET ☺ 1 → (E) 6 T id Closure of Grammer with E' as start Symbol EE+T E EXT T T .(E) .id Trasition 1 Transition 2 - Transition 3 Transition 4 Transition 5 & ' E.} { [ E. & T} & E.XT } E T. } 9 T l .E E . ETT E SEAT ET

Transition 6 S T sid. } Transion 7 - EE+ T .CE Tid Transition 8 ss & E T ? T . (E) T id Transition 9 S E +T. I ansion 10 SEMENT.} Transition 11 &T (E.) } Transitioni2 —>$T (E).}

E ESE 3, Accept e > E-C til + EE+:1 . EAT . EAT E - E EE+T EE+T T . (E) Tid آ (٤) رج Tid CEE XT 13 Е -Т. 110 E. ESTEST) -> EAT. T id. 16 T (E) deid, 28 T CE. I Et7. 39 an (E). 1.2

LR10) Parse Table Goto Action Toids Io - I2 Iz Iy 13 Is 825 Iz 18 19. 12 512 W In the table Ro) represent that broduchon Passe Table the state is outcome of to si represents to that the respective shift happens non-terminal ith state dut v Main Libra

bottom up passing (id+ id) id I lid + id | 2 4 | id | & input stack Look Tu Ahead! $1 Parse stack Step 1 Push and innement look ahead Sympel [id] + | id ) ) ) * ] id I to T look e Stack shead + liel? | id) $ I id replaced t id Step 3

replace T id replace T (E) replace id EET HA Generabe paise ree th? ( id + id) & id DUTERTE