Compiling: Examples and Sample Problems

Transcription

1 REs for Kywors Compiling: Exmpls n mpl Prolms IC312 Mchin-Lvl n ystms Progrmming Hnri Csnov (hnric@hwii.u) It is sy to fin RE tht scris ll kywors Ky = if ls for whil int.. Ths cn split in groups if n Kywor = if ls for Typ = int oul long Th choic pns on wht th nxt componnt (i.., th prsr) woul lik to s RE for Numrs RE for Intifirs trightforwr rprsnttion for intgrs igits = intgr = igits + RE systms llow th us of - for rngs, somtims with [ n ] igits = [-9]+ Floting point numrs r much mor complict 2.,.12-12, 312.1E+12, 4, Hr is on ttmpt Hr is typicl scription lttr = -z -Z int = lttr ( lttr igit _ ) * trts with lttr Hs ny numr of lttr or igit or _ ftrwrs In C: int = (lttr _ ) (lttr igit _ ) * ( + - )(igit +.? igits * (. igit + )) (( E )( + - ) igit+)))? Not th iffrnc twn mt-chrctr n lngugchrctrs + vrsus +, - vrsus -, ( vrsus (, tc. Oftn ooks/ocumnttions us iffrnt fonts for ch lvl of lngug

2 RE for Phon Numrs impl RE igit = -9 r = igit igit igit xchng = igit igit igit locl = igit igit igit igit phonnumr = ( r )? xchng ( - ) locl Th ov scris th strings of th L(phonnumr) lngug Rgulr ssion Prctic Writ rgulr xprssions for ll strings ovr lpht {,,c} ll strings ovr lpht {,,c} tht contin sustring c ll strings ovr lpht {,,c} tht consist of on or mor s, follow y two s, follow y whtvr squnc of s n c s ll strings ovr lpht {,,c} such tht thy contin t lst on of sustrings c or c Rgulr ssion Prctic Writ rgulr xprssions for ll strings ovr lpht {,,c} ( c)* ll strings ovr lpht {,,c} tht contin sustring c ( c)*c( c)* ll strings ovr lpht {,,c} tht consist of on or mor s, follow y two s, follow y whtvr squnc of s n c s + ( c)* ll strings ovr lpht {,,c} such tht thy contin t lst on of sustrings c or c (( c)*c( c)* ( c)*c( c)*) utomton Exmpls f i n s1 s2 This utomton ccpts input if

3 utomton Exmpls n 1 s1 This utomton ccpts strings tht strt with, thn hv ny numr of 1 s, n n with Not th nturl corrsponnc twn utomt n REs: 1 * Qustion: cn w rprsnt ll REs with simpl utomt? nswr: ys Thrfor, if w writ pic of co tht implmnts ritrry utomt, w hv pic of co tht implmnts ritrry REs, n w hv lxr! Not _this_ simpl, ut clos s2 Exmpl REs n DF y w wnt to rprsnt RE * * c * * with DF n s1 c c c s2 s3 s4 Exmpl REs n NF * * c * * : much simplr with NF Exmpl REs n NF + + c + + : sy moifiction n s1 s2 c s3 s4 n c c s1 s2 s3 s4 s5 With -trnsitions, th utomton cn choos to skip h, non-trministiclly But now w hv multipl choics for givn chrctr t ch stt!.g., two rrows lving n

4 utomton vs. RE Prctic Writ REs for th following NFs utomton vs. RE Prctic Writ REs for th following NFs + * **( *) **(* + ) Grmmr for ssions Op Numr Intifir Intifir Lttr Lttr Intifir Lttr -z Op + - * / Numr Digit Numr Digit Digit Op Numr Op Digit Numr Op 3 Numr Op 34 Op 34 * 34 * Intifir 34 * Lttr Intifir 34 * Intifir 34 * Lttr 34 * x Drivtions s Trs convnint n nturl wy to rprsnt squnc of rivtions is syntctic tr or prs tr Exmpl: Op Numr Op Digit Numr Op 3 Numr Op 34 Op 34 * 34 * Intifir 34 * Lttr Intifir 34 * Intifir 34 * Lttr 34 * x Digit 3 Numr Numr Digit 4 Op * Lttr Intifir Intifir Lttr x

5 Drivtions s Trs In th prsr, rivtions r implmnt s trs Oftn, w rw trs without th full rivtions Exmpl: Grmmr Prctic Consir th CFG: ( L ) L L, Numr Op * Intifir Drw prs trs for: (, ) (, ((, ), (, ))) 34 x Grmmr Prctic Grmmr Prctic ( L ) Consir th CFG: ( L ) L L, ( L ) Consir th CFG: ( L ) L L, L, ( L ) L, Drw prs trs for: (, ) (, ((, ), (, ))) L, Drw prs trs for: (, ) (, ((, ), (, ))) ( L ) ( L ) L, L,

6 Grmmr Prctic Writ CFG for th lngug of wll-form prnthsiz xprssions (), (()), ()(), (()()), tc.: OK ()), )(, ((()), (((, tc.: not OK Grmmr Prctic Writ CFG for th lngug of wll-form prnthsiz xprssions (), (()), ()(), (()()), tc.: OK ()), )(, ((()), (((, tc.: not OK P () PP (P) Grmmr Prctic Is th following grmmr miguous? n not 1 Grmmr Prctic Is th following grmmr miguous? n not 1 not Ys! n n not 1 1