LR(0) Analysis. LR(0) Analysis

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1 LR() Analysis LR() Conlicts: Introuction Whn constructing th LR() analysis tal scri in th prvious stps, it has not n possil to gt a trministic analysr, caus thr ar svral possil actions in th sam cll. I this happns, w shall say that th grammar is not LR(). Othrwis, w shall say that th grammar is LR(). Th xistnc o non-trminism is call conlict Conlicts can o any o ths two kins: Shit / ruc conlicts: In this cas thr ar shit an ruc actions in th sam cll. Th last xrcis contains an xampl o on o ths conlicts. Ruc / ruc conlicts: In this cas all th actions in th cll ar ruc actions. Th conlict consists in that w o not know orhan which rul w shoul ruc or pting th input string. LR() Analysis LR() Conlicts: Possil solutions vn i th grammar is not LR(), in many cass it is not iicult to imagin a solution or th prolm: W shall analys th conlict in th xampl: although w can in a rivation tr or th string, th symol provoks that thr ar two possil actions. <lock> Shit Ruction <cs> <jcs> <jcs> gin c jc jc n

2 LR() Analysis LR() Conlicts: Possil solutions W might not, howvr, that th ruc opration will not prmit a corrct analysis i th string, caus th only symol that can ollow <jcs> is n. I w ruc th rul, th symol ollowing <jcs> woul an, oring to th grammar, that is impossil. Thror, th only possil action to tak is th shit. <lock> Shit <cs> <jcs> <jcs> gin c jc jc n SLR() Analysis Introuction SLR() analysis is an improv vrsion o LR() analysis that: Shars with LR() th tchniqu or crating stats. Thror, It mploys th sam algorithm or th closur opration It mploys th sam algorithm or th go-to opration It uss th analysis tal in th sam way. It ills in th clls with th shit oprations in th sam way. On th othr han, it has th ollowing irnc: It taks into ount that ructions can only happn or trminal symols that may ollow th non-trminal in th grammar.

3 SLR() Analysis Construction o SLR() Analysis tals Concrning shits an ructions, Shit actions in th tal: Thy ar on xactly as in LR() Thy ar otain y ollowing th transitions in th automaton. In othr wors, i thr is a transition in th automaton rom s i to s j with th symol X, thn w a th action Tal[i,X]= sj i X j i X Ructions in th tal: For ach o th stats which contain a ruction coniguration (on o th typ A γ ) w hav to a th rul A γ only in th columns or th trminal symols that can ollow th non-trminal at th lt-han si o th rul (A). Thror, this stp is irnt to LR() SLR() Analysis Construction o SLR() Analysis tals Accptation: It is th sam as in LR() I a stat s i has a transition, with th trminal to th stat with th ruction o th nw rul axiom axiom Thn w a to Tal[i,]th action pt Thr xist variations o this approach. rror: It is th sam as in LR() All th rmaining clls hav associat th action rror Th most common is to lav thm mpty.

4 SLR() Analysis Construction o SLR() Analysis tals Th ollowing is th analysis tal or th xrcis It is asy to chck that, in this grammar, () () () () () () Th ollowing trminal symols can ollow ach nontrminal. nxt() = {} nxt()= {} nxt()= {} s s r s s s r r r SLR() Analysis Construction o SLR() Analysis tals Chck that th tal is corrct with th ollowing xampl programs: Corrct: gin c jc jc n Incorrct: gin c jc n

5 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

6 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

7 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

8 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

9 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

10 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

11 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

12 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

13 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

14 SLR() Analysis () () () () () () r r r s r s s s s SLR() Analysis () () () () () () r r r s r s s s s

15 SLR() Analysis s r s s s s r r r () () () () () () SLR() Analysis Concpts Whn uiling th SLR() analysis tal, as scri in th prvious points, it may th cas that w cannot otain a trministic grammar (caus thr is mor than on action in som cll). In this cas, w shall say that th grammar is not SLR() Othrwis, w shall say that th grammar is SLR().

Othr analysis algorithms Introuctory xampl uil th SLR() analysis tal or th ollowing grammar: {x, a n x n n } ()S A ()S x ()A aa ()A () x Th irst thing to o is to xtn th grammar:

16 Othr analysis algorithms Introuctory xampl uil th SLR() analysis tal or th ollowing grammar: {x, a n x n n } ()S A ()S x ()A aa ()A () x Th irst thing to o is to xtn th grammar: ()S S ()S A ()S x ()A aa ()A () x Othr analysis algorithms Introuctory xampl W calculat th iagram with th stats an transitions o th SLR() parsr ()S S ()S A ()S x ()A aa ()A () x

17 An th SLR() analysis tal Othr analysis algorithms Introuctory xampl a x S A s ()S S ()S A ()S x ()A aa ()A () x r r/s s r r r r r r Othr analysis algorithms Introuction Thr ar high-lvl programming with grammars which ar not SLR() In ths cass, it is possil to us mor powrul algorithms. W ar going to s th ollowing two: LR(k),, k LALR()

18 Othr analysis algorithms xampl uil th SLR() analysis tal o th ollowing amiguous grammar that gnrats arithmtic xprssions: () + () * () i Th irst thing to o is to augmnt th grammar: () () + () * () i Othr analysis algorithms xampl W calculat th SLR() iagram with th transitions twn stats () () + () * () i

19 An th SLR() Othr analysis algorithms xampl * + i s () () + () * () i s s s r/s r/ r r/s r/ r This grammar is not SLR() Othr analysis algorithms xampl: possil solutions Th prolm was originat y th ollowing amiguity: (i+i)*i or i+(i*i)?) I this happns, a possil solution is to orc on cision among th svral that may in th clls. ar in min that th cision takn will act th prcnc o th oprators:

20 Othr analysis algorithms xampl: possil solutions I w shit with + an ruc with *... * + i s () () + () * () i s s s r r r r Othr analysis algorithms xampl: possil solutions This woul th analysis o th ollowing string i*i+i*i+i

21 Othr analysis algorithms xampl: possil solutions IF w shit with * an ruc with +... * + i s () () + () * () i s s s s r r s r r This is th analysis o i*i+i*i+i Othr analysis algorithms xampl: possil solutions

22 ottom-up Analysis Glossary LR(k): Tchniqu or ottom-up syntactic analysis xamins th ntry lt-to-right uils a right-most rivation o th ntry It uss th k tokns in th input that ollow th currnt symol. SLR: Tchniqu or ottom-up analysis which is a simpliication o LR(k). Acronym or Simpl Lt-to-Right LALR: ottom-up tchniqu, similar to LR, which uss anticipation symols. Acronym or Look-Aha Lt-to-Right. Syntactic Analysis iliography [Al] Toría Autómatas y lnguajs ormals M. Alonsca y otros [Hop] Introucción a la toría autómatas, lnguajs y computación Hopcrot, J. Motwani, R. Ullman, J. [Aho] Compilaors. Principios, técnicas y hrramintas A. V. Aho R. Sthi J.. Ullman

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages: CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings