CMSC 430, Practice Problems 1 (Solutions)

Transcription

1 CMC 430, Prtie Problems 1 olutios) 1. Cosider the followig grmmr: d or ) true flse. Compute First sets for eh produtio d otermil FIRTtrue) = { true } FIRTflse) = { flse } FIRT ) ) = { } FIRT d ) = FIRT or ) = FIRT ) = {, true, flse } b. Expli why the grmmr ot be prsed by LL1) prser First sets of produtios iterset, grmmr is left reursive 2. Cosider the followig grmmr: b. Compute First sets for eh produtio d otermil FIRTb) = { } FIRT) = { } FIRT) = { } FIRT) = {, } b. how why the grmmr ot be prsed by LL1) prser. First sets of produtios overlp FIRTb) FIRT) = { } { } = { }. Rewrite the grmmr so it be prsed by LL1) prser. L L b 3. Cosider the followig grmmr:. how why the grmmr ot be prsed by preditive prser. First sets of produtios iterset, grmmr is left reursive b. Rewrite the grmmr so it be prsed by preditive prser. L L L L ε. Usig FIRT d FOLLOW, build the LL1) tble for the ew grmmr FIRT L ε) = FOLLOWL) = {$} $ L L L L L L L ε d. Usig the LL1) tble, show how tble-drive prser prses the strig tk Iput tio [$, ] $ L, pop push L [$, L, ] $ ext iput pop [$, L] $ L L, pop L push L [$, L, ] $ ext iput pop [$, L] $ L L, pop L push L [$, L, ] $ ext iput pop [$, L] $ L L, pop L push L [$, L, ] $ ext iput pop [$, L] $ L ε, pop L [$] $ ept

2 4. Cosider the followig grmmr Gol Expr Expr Term Expr Term Expr Term Term Ftor Term Ftor / Term Ftor Ftor um id. pply left ftorig to rete LL1) grmmr b. Compute FIRT d FOLLOW for the modified grmmr Left Ftored Grmmr FIRT FOLLOW Produtios Notermils Gol Expr { um, id } Gol { um, id } { $ } Expr Term Expr { um, id } Expr { um, id } { $ } Expr Expr { } Expr {, -, ε } { $ } Expr { } Term { um, id } {, -, $ } ε { ε } Term {, /, ε } {, -, $ } Term Ftor Term { um, id } Ftor { um, id } {, /,, -, $ } Term Term { } / Term { / } ε { ε } Ftor um { um } id { id }. Usig FIRT d FOLLOW, build the LL1) tble for the ew grmmr um id - / $ Gol Expr Gol Expr Expr Term Expr Gol Expr Expr Term Expr Expr Expr Expr Expr - Expr Expr ε Term Term Ftor Term Term Ftor Term Term Term ε Term ε Term Term Term / Term Term ε Ftor Ftor um Ftor id

3 5. ottom up prsig. Desribe the differee betwee bottom-up d top-dow prsig with respet to grmmr produtio β ottom up prsers perform redutios of β to, while top-dow prsers perform expsios of to β. b. Defie hdle The right-hd side of the ext produtio to be redued i the rightmost derivtio, d its positio i the urret setetil form.. Expli why bottom-up prsers result i right-most derivtios i reverse. euse iput is proessed from left to right d uproessed iput is omposed oly of termils, right-most derivtio is used so the setetil form to the right of the hdle is omposed etirely of termils. d. Give the followig CTION/GOTO tble, perform prse of, ssumig 0 is the strt stte. how the otets of the stk, remiig iput, d tio performed t eh step of the shift-redue prse. 6. LR prsig. Wht is the oil set of LRk) items for grmmr? determiisti fiite utomto DF) for reogizig hdles right-hd sides of produtios) for the grmmr. b. Wht re CTION/GOTO tbles of LRk) prser for grmmr? Tbles eodig the DF for reogizig hdles for the grmmr.. Give LRk) item [ α γ, δ] from produtio β, desribe the role of, α, γ, δ is the otermil tht is potetilly the result of redutio. α is the portio of β tht the prser hs just see. γ is the portio of β the prser will eed to see before performig the redutio to. δ is k termils tht must be the k lookheds for the redutio to be performed.

4 d. Give LRk) item [ α γ, δ], wht lookhed llows shift to be performed igorig y other LRk) items dded to the stte by losure)? The termil t the begiig of γ. e. Give LRk) item [ α γ, δ], wht LRk) items must be dded to the losure? y produtio for the otermil t the begiig of γ, with t the begiig of the right-hd side of the produtio, d FIRTγ δ) s the lookhed toke, where γ is wht remis i γ fter removig the first. f. If the prser is i stte otiig LRk) item [ α γ, δ], wht must be t the top of the stk, d why? The top of the stk must be α, sie the prser just sw α. g. Desribe wht ostitutes shift/redue oflit DF stte otis both LR items llowig shift d redue for the sme lookhed. h. Give exmple of two LR1) items usig redue/redue oflit. [ α, δ] d [ α, δ] i. Expli why there re o shift/shift oflits euse o deisio eeds to be mde bout whih right-hd side of produtio is the hdle. 7. LLR prsig. Cosider the followig sets of LR1) items i the sttes of LR1) prser.. Fid ll shift/redue d redue/redue oflits. List the LR1) items d lookheds usig oflits. hift/redue oflit is used by [, ] d [, ] o lookhed i stte 2. b. Wht sttes would be merged i LLR1) prser? ttes 0 d 2.. re y ew redue/redue oflits itrodued i the LLR1) prser? /redue oflit is used by [, b] d [, b] o lookhed b i the merged stte. d. Expli why LLR1) prsers will ot itrodue ew shift/redue oflits. euse the ore of ll merged sttes must be idetil, the LR item for the shift must hve bee i ll of the sttes prior to the merge. y LR item usig redue must hve ome from some stte, d the sme shift/redue oflit would hve existed i tht stte.

5 e. Wht is the reltioship betwee LLR1) d LR1) prsers? LLR1) prsers re stritly more powerful th LR1) prsers, so y grmmr tht be prsed by LR1) prser my be prsed by LLR1) prser, but there re grmmrs tht be prsed by LLR1) prsers tht ot be prsed by LR1) prsers. 8. Cosider the followig grmmr: b. Compute FOLLOW) FOLLOW) = { $ } b. Compute the oil set of LR0) items for the grmmr tte 0 [ ] [ b] [ ] [ ] tte 1 [ ] tte 2 [ ] b tte 4 [ b ] [ b] [ ] [ ] tte 3 [ b] [ ] tte 6 [ b ] tte 5 [ ] [ b] [ ] [ ] tte 7 [ ]. uild the CTION/GOTO tble usig LR0) FOLLOW tio Goto tte b $ 0 hift 3 hift ept 2 3 hift 4 hift 5 4 hift 3 hift hift 3 hift b 7 d. Expli why the grmmr is or is ot LR1) It is LR1) sie the LR1) CTION/GOTO tble hs o oflits.

6 e. Use the CTION/GOTO tble to prse the strig b tk Remiig Iput tio Commet $ 0 b $ hift 3 $ 0 3 b $ hift 4 $ 0 3 b 4 $ hift 2 $ 0 3 b 4 2 $ $ 0 3 b 4 $ Goto 6 Itermedite tep $ 0 3 b 4 6 $ b $ 0 $ Goto 1 Itermedite tep $ 0 1 $ ept 9. Cosider the followig grmmr:. Compute the oil set of LR1) items for the grmmr tte 0 [, $ ] [, {$,,} ] [, {$,,} ] [, {$,,} ] tte 1 [, {$,,} ] tte 2 [, $ ] [, {$,,} ] [, {$,,} ] tte 3 tte 4 [, {$,,} ] [, {$,,} ] b. uild the CTION/GOTO tble for the grmmr tio Goto tte $ 0 hift hift 3 hift 4 ept 3 4. Expli why the grmmr is or is ot LR1) It is LR1) sie the LR1) CTION/GOTO tble hs o oflits.

7 d. Use the CTION/GOTO tble to prse the strig tk Remiig Iput tio Commet $ 0 $ hift 1 $ 0 1 $ $ 0 $ Goto 2 Itermedite tep $ 0 2 $ hift 3 $ $ $ 0 $ Goto 2 Itermedite tep $ 0 2 $ hift 4 $ $ $ 0 $ Goto 2 Itermedite tep $ 0 2 $ hift 3 $ $ $ 0 $ Goto 2 Itermedite tep $ 0 2 $ ept 10. Cosider the followig grmmr: ) um. Compute the oil set of LR1) items for the grmmr tte 3 [, $ ] [, {$,,} ] [, {$,,} ] tte 1 [, {$,,}] tte 14 [, {$,,} ] [, {$,,} ] [, {$,,} ] [ ), {$,,} ] [, {$,,} ] tte 15 [, {$,,} ] [, {$,,} ] [, {$,,} ] [ ), {$,,} ] [, {$,,} ] tte 16 [, {$,,} ] [, {$,,} ] [, {$,,} ] tte 17 [, {$,,} ] [, {$,,} ] [, {$,,} ] tte 8 [ ), { ),,} ] [, { ),,} ] [, { ),,} ] ) tte 9 [ ), { ),,} ] tte 0 [, $ ] [, {$,,} ] [, {$,,} ] [ ), {$,,} ] [, {$,,} ] tte 6 [ ), { ),,} ] [, { ),,} ] tte 2 [, { ),,} ] [ ), { $,,} ] [ ), { ),,} ] [, { ),,} ] [, { ),,} ] [, { ),,} ] [ ), { ),,} ] [, { ),,} ] tte 4 [, { ),,} ] tte 5 [ ), {$,,} ] [, { ),,} ] [, { ),,} ] ) tte 7 [ ), {$,,} ] tte 10 [, { ),,} ] [, { ),,} ] [, { ),,} ] [ ), { ),,} ] [, { ),,} ] tte 11 [, { ),,} ] [, { ),,} ] [, { ),,} ] [ ), { ),,} ] [, { ),,} ] tte 12 [, { ),,} ] [, { ),,} ] [, { ),,} ] tte 13 [, { ),,} ] [, { ),,} ] [, { ),,} ]

8 uild the CTION/GOTO tble for the grmmr tio Goto tte ) um $ 0 hift 2 hift um um um 2 hift 6 hift hift 14 hift 15 ept 4 um um um 5 hift 10 hift 11 hift 7 6 hift 6 hift ) ) ) 8 hift 10 hift 11 hift 9 9 ) ) ) 10 hift 6 hift hift 6 hift hift 10 hift hift 10 hift hift 2 hift hift 2 hift hift 14 hift hift 14 hift 15 b. Expli why the grmmr is or is ot LR1) It is ot LR1) beuse there re shift/redue oflits i sttes 16 & 17 d 12 & 13) for lookhed d.

9 . Expli how to use the CTION/GOTO tble so tht Lookhed tte o left or shift o right oto stk? Depeds o ssoitivity of shift if right sso, redue if left) 16 o stk 17 o stk o left or shift o right oto stk? Depeds o preedee of vs shift if >, redue if < ) o left or shift o right oto stk? Depeds o preedee of vs shift if >, redue if < ) o left or shift o right oto stk? Depeds o ssoitivity of shift if right sso, redue if left) i. hs higher preedee th d, re both left ssoitive Resolve the shift/redue oflits s follows sme for 12 & 13).. Lookhed tte 16 hift ii. hs higher preedee th, is left ssoitive, d is right ssoitive Resolve the shift/redue oflits s follows sme for 12 & 13).. Lookhed tte 16 hift 14 hift iii. hs higher preedee th d, re both right ssoitive Resolve the shift/redue oflits s follows sme for 12 & 13). Lookhed tte 16 hift hift 14 hift Cosider the followig grmmr: b. Compute the oil set of LR0) items for the grmmr b. uild the CTION/GOTO tble for the grmmr. Compute the oil set of LR1) items for the grmmr d. uild the CTION/GOTO tble for the grmmr ee solutio for problem 8 t

10 12. Cosider the followig grmmr: ;. how the grmmr is LR1) but ot LR1) LR1) prser? FOLLOW ) = { $ } FOLLOW) = { $, ; } Coil set of LR0) items = tte 0 [ ] [ ; ] [ ] tte 2 [ ] [ ; ] ; tte 1 [ ] tte 3 [ ; ] tte 4 [ ; ] tio Goto tte ; $ 0 hift hift 3 ept 3 hift 4 4 ; ; No oflits i y stte, grmmr is LR1) LR1) prser? Coil set of LR1) items = tte 0 [, $ ] [ ;, {$,;} ] [, {$,;} ] tte 2 [, $ ] [ ;, {$,;} ] ; tte 1 [, {$,;} ] tte 3 [ ;, {$,;} ] tte 4 [ ;, {$,;} ] No oflits i y stte, grmmr is LR1) ltertive proof: ie grmmr is LR1), it must be lso LR1) sie LR1) is superset of LR1).

11 13. Cosider the followig grmmr: d bd e be. how the grmmr is LR1) but ot LLR1) LR1) prser? Coil set of LR1) items = tte 0 [, $ ] [ d, $ ] [ bd, $ ] [ e, $ ] [ be, $ ] tte 1 [, $ ] tte 2 b [ b d, $ ] [ b e, $ ] [, e ] [, d ] tte 3 [ d, $ ] [ e, $ ] [, d ] [, e ] tte 4 d tte 5 [ b d, $ ] [ bd, $ ] tte 6 e tte 7 [ b e, $ ] [ be, $ ] tte 8 [, e ] [, d ] tte 9 d tte 10 [ d, $ ] [ d, $ ] tte 11 [ e, $ ] e tte 12 [ e, $ ] tte 13 [, d ] [, e ] No oflits i y stte, grmmr is LR1) LLR1) prser? ttes 8 & 13 merged sie they hve idetil ores, yieldig tte 0 [, $ ] [ d, $ ] [ bd, $ ] [ e, $ ] [ be, $ ] tte 1 [, $ ] b tte 2 [ b d, $ ] [ b e, $ ] [, e ] [, d ] tte 3 [ d, $ ] [ e, $ ] [, d ] [, e ] tte 4 [ b d, $ ] tte 6 [ b e, $ ] tte 8 [, {d,e} ] [, {d,e} ] tte 9 [ d, $ ] tte 11 [ e, $ ] d tte 5 [ bd, $ ] e tte 7 [ be, $ ] d tte 10 [ d, $ ] e tte 12 [ e, $ ] Not LLR1), redue/redue error i tte 8 o lookheds d,e

12 14. Cosider the followig grmmr: b b d d. how the grmmr is LR1) but ot LLR1) LR1) prser? Coil set of LR1) items = tte 0 tte 1 [, $ ] b [ b, $ ] [, $ ] [ b, $ ] [ b, $ ] [ d, ] [, $ ] [ d, ] [ b, $ ] d [ d, ] tte 7 [ d, ] [ d, ] [ d, ] tte 8 [, $ ] tte 2 [ b, $ ] tte 4 [ b, $ ] d tte 6 [ d, ] [ d, ] tte 9 [, $ ] tte 3 [ b, $ ] tte 5 [ b, $ ] tte 12 [, $ ] tte 10 [, $ ] tte 11 [, $ ] No oflits i y stte, grmmr is LR1) LLR1) prser? ttes 6 & 7 merged sie they hve idetil ores, yieldig tte 0 [, $ ] [, $ ] [ b, $ ] [, $ ] [ b, $ ] [ d, ] [ d, ] tte 1 b [ b, $ ] [ b, $ ] [ d, ] d [ d, ] tte 6 [ d, {,} ] [ d, {,} ] tte 8 [, $ ] tte 2 [ b, $ ] tte 4 d [ b, $ ] tte 9 [, $ ] tte 3 [ b, $ ] tte 5 [ b, $ ] tte 12 [, $ ] tte 10 [, $ ] tte 11 [, $ ] Not LLR1), redue/redue error i tte 6 o lookheds,