Pattern Matching. Pattern Matching. Pattern Matching. Review of Regular Expressions

Transcription

1 Pttern Mthing Pttern Mthing Some of these leture slides hve een dpted from: lgorithms in C, Roert Sedgewik. Gol. Generlize string serhing to inompletely speified ptterns. pplitions. Test if string or its sustring mthes some pttern. vlidte dt-entry fields (dtes, emil, URL, redit rd) text filters (spm, NetNnny, Crnivore) omputtionl iology Prse text files. given we pge, extrt nmes of ll links (we rwling, indexing, nd serhing) Jvdo: utomtilly rete doumenttion from omments Reple or sustitute some pttern in text string. text-editor remove ll tgs in we pge, leving only ontent Pttern Mthing Review of Regulr Expressions Gol. Generlize string serhing to inompletely speified ptterns. Text. N hrters. Pttern. M hrter REGULR EXPRESSION. Compt nd expressive nottion for desriing text ptterns. lgorithmilly interesting. Esy to implement. Mthing. Does the text mth the pttern? Serh. Find sustring of the text tht mthes the pttern. Serh ll. Find ll sustrings of the text tht mth the pttern. Theoretiin. Lnguge epted y FS. Progrmmer. Compt desription of multiple strings. You. Prtil pplition of ore CS priniples. Contente. d d Logil OR. +, ( + )( + d), d,, d Closure. *,,,,,, *,,,,, ( + )* d d, d, d, d, d, d, 5 6

2 Pttern Mthing nd You FS nd RE Brodly pplile progrmmer s tool. Mny lnguges support extended regulr expressions. Built into Perl, PHP, Python, JvSript, ems, egrep, wk. Find ny + letter words in ditionry tht n e typed y using only top row letters, followed y ottom row letters. Kleene s theorem (56). FS nd RE desrie sme lnguges. Possile grep implementtion. Build FS from RE. Write C progrm to simulte FS. Performne rrier: FS n e exponentilly lrge. egrep ^[qwertyuiop]*[zxvnm]*$ /usr/dit/words egrep... perl -ne print if /^[qwertyuiop]*[zxvnm]*$/ /usr/dit/words perl -ne print if /.../! typewritten tul grep implementtion. Build nondeinisti FS from RE. Write C progrm to simulte NFS. Essentil prdigm in omputer siene. Build inedite strtions. Pik the right ones! Stephen C. Kleene (0 - ) Review of NFS Simulting n NFS nondeinisti FS. 0,, or rs leving stte, eh with sme lel. - trnsitions llowed, ut no - yles. Note: this restrited form is no loss of generlity. Brute fore. Try ll possile pths exponentil time. Better ide. Keep trk of ll possile sttes NFS ould e in fter reding in first i hrters. Use deque (doule-ended queue). n push/pop like stk, enqueue like queue d possile sttes fter i hrs Deque 5 possile sttes NFS ould e in fter i hrs Pop stte v. if lel of r v w is, push stte w (* + )d if urrent hrter mthes lel, enqueue stte w if mismth, ignore 0

3 NFS Simultor Performne Goth #define SCN #define EPS #define MTCHSTTE 0 nfs() int mth(hr []) { int j = 0, stte = next[0]; DQinit(); DQput(SCN); while(stte!= MTCHSTTE) { if (stte == SCN) { DQput(sn); else if (h[stte] == [j]) { DQput(next[stte]); else if (h[stte] == EPS) { DQpush(next[stte]); DQpush(next[stte]); if (DQisempty() [j] == \0 ) return 0; stte = DQpop(); return j; Mjor performne ug if not reful. Simulte input on NFS. 0 Duplite sttes llowed on deque exponentil growth! Esy fix. 5 (*)* Disllow duplite sttes on sme side of deque. Keep "existene rry" of sttes urrently on eh side of deque. 6 5 Deque... Build NFS from RE Prse Tree Gol: uild NFS from RE. First hllenge: Is expression legl RE? Use ontext free lnguge to desrie RE. Prse tree: grmmtil struture of string. Prser: onstrut tree. Exmple: (* + )d. expr ftr Strt : <expr> Strt : <expr> ( expr ) ftr <expr> <expr> <> <> + <expr> <expr> <expr> <> <> + <expr> + expr <> <> <ftr> <ftr><> <> <> <ftr> <ftr><> ftr <ftr> <ftr> * <ftr> (<expr>) <ftr> (<expr>)* <ftr> <ftr> * <ftr> (<expr>) <ftr> (<expr>)* * ftr ftr ftr

4 Reursive Desent Prser for RE Top-down reursive desent prser: Reursive progrm diretly derived from CFL. min() int j = 0; // urrent index hr p[mxn + ]; // RE pttern void prserror(void) { printf("%s is not RE.\n", p); exit(exit_filure); int min(void) { snf("%s", p); ; if (j!= strlen(p)) prserror(p); return 0; Reursive Desent Prser for RE Definition of expression in CFL. <expr> <> <expr> <> + <expr> Definition of in CFL. <> <ftr> <> <ftr> <> void { ; if (p[j] == + ) { ; void { ftr(); if ((p[j] == ( ) islower(p[j])) ; 5 6 Reursive Desent Prser for RE Left Reursive Prsers Definition of ftor in CFL. <ftr> <ftr> * <ftr> (<expr>) <ftr> (<expr>)* void ftr() { if (islower(p[j])) { else if (p[j] == ( ) { ; if (p[j] == ) ) else prserror(); else prserror(); ftor() if (p[j] == * ) Not s trivil s it first seems. lternte definition of expr in CFL. <expr> <expr> <expr> + <> Fix: use left reursive CFL. d void d { if (islower(p[j]) else { d; if (p[j] == + ) { ; else prserror(); voiding infinite reursive loops is fundmentl diffiulty in reursive-desent prsers. Prolem n e more sutle thn exmple ove.

5 Left Reursive Prsers Building NFS from RE Exmple. (* + )d. Corresponds to prse tree. Unix ftr() ( ftr() * ftr() + ftr() ftr() ) ftr() d Eh RE onstrut orresponds to piee of NFS. Single hrter. strt Contention. B B OR. + B B Closure. * ept B B 0 Building NFS from RE: Exmple Building NFS from RE: Exmple Eh RE onstrut orresponds to piee of NFS. (* + )d Eh RE onstrut orresponds to piee of NFS. (* + )d *

6 Building NFS from RE: Exmple Building NFS from RE: Exmple Eh RE onstrut orresponds to piee of NFS. (* + )d Eh RE onstrut orresponds to piee of NFS. (* + )d 5 5 * * Building NFS from RE: Exmple Building NFS from RE: Exmple Eh RE onstrut orresponds to piee of NFS. (* + )d Eh RE onstrut orresponds to piee of NFS. (* + )d * * 5 6

7 Building NFS from RE: Exmple Building NFS from RE: Exmple Eh RE onstrut orresponds to piee of NFS. (* + )d Eh RE onstrut orresponds to piee of NFS. (* + )d * * + Building NFS from RE: Exmple Building NFS from RE: Exmple Eh RE onstrut orresponds to piee of NFS. (* + )d Note. This onstrution doesn t yield simplest NFS. (* + )d 0 6 d 5 d (* + )d 0

8 Building NFS from RE: Theory Building NFS from RE: Prtie For ny RE of length M, our onstrution produes n NFS with the following properties. No more thn two rs leve ny stte. if two rs, they oth hve lel No - yles. Extly strt stte, hs inoming r. Extly ept stte, hs t most leving r. Numer of sttes M. Proof: pply omposition rules nd use indution on length of RE. For numer of sttes. single hrter: ontention B: + B losure *: + OR + B: + B + To uild NFS, ugment prser to generte stte tle. For detils: Sedgewik, Chpter (lgorithms in C, nd edition). reursive routines return index of strt stte stte = next stte to e filled in setstte() fills in NFS tle int { int s, s, strt; strt = s = ; if (p[j] == + ) { strt = s = ++stte; stte++; setstte(s, EPS,, s); setstte(s, EPS, stte, stte); return strt; Complexity nlysis Perspetive Text. N hrters. Pttern. M hrter regulr expression. Mthing: Does the text mth the pttern? Build NFS. t most M sttes O(M) time, O(M) spe Simulte NFS. O(M) time per text hrter euse of -trnsitions O(MN) time, O(M) spe. Serh: Find sustring of the text tht mthes the pttern. For eh offset of text, solve mthing prolem. Compiler. progrm tht trnsltes from one lnguge to nother. Grep: RE NFS. C ompiler: C lnguge mhine lnguge. strt Mhine NFS Computer Pttern Word in CFL Word in CFL Prser Chek if legl RE Chek if legl C progrm Compiler Output NFS Output mhine exeutle Simultor Find mth Run progrm in hrdwre O(MN ) time, O(M+N) spe.