7. Theory of Computation. Regular Expressions. Introduction to Theoretical CS. Why Learn Theory?

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1 Introduction to Theoreticl CS 7. Theory of Computtion Q. Wht cn computer do? Q. Wht cn computer do with limited resources? Generl pproch. Don't tlk out specific mchines or prolems. Consider miniml strct mchines. Consider generl clsses of prolems. e.g., Intel Core 2 Duo running Linux kernel 2.6 Pioneering work in the 1930s. Princeton == center of universe. Automt, lnguges, computility, universlity, complexity, logic. Introduction to Computer Science Roert Sedgewick nd Kevin Wyne Copyright 2008 * * Dvid Hilert Kurt Gödel Aln Turing Alonzo Church John von eumnn 2 Why Lern Theory? In theory Deeper understnding of wht is computer nd computing. Foundtion of ll modern computers. Pure science. Philosophicl implictions. Regulr Expressions In prctice We serch: theory of pttern mtching. Sequentil circuits: theory of finite stte utomt. Compilers: theory of context free grmmrs. Cryptogrphy: theory of computtionl complexity. Dt compression: theory of informtion. In theory there is no difference etween theory nd prctice. In prctice there is. Yogi Berr 3

2 Descriing Pttern Pttern Mtching Applictions PROSITE. Huge dtse of protein fmilies nd domins. Q. How to descrie protein motif? Ex. [signture of the C 2 H 2 -type zinc finger domin] C Between 2 nd 4 mino cids. C 3 more mino cids. One of the following mino cids: LIVMFYWCX. 8 more mino cids. H Between 3 nd 5 more mino cids. H Test if string mtches some pttern. Process nturl lnguge. Scn for virus signtures. Access informtion in digitl lirries. Serch-nd-replce in word processors. Filter text (spm, etnny, ds, Crnivore, mlwre). Vlidte dt-entry fields (dtes, emil, URL, credit crd). Serch for mrkers in humn genome using PROSITE ptterns. Prse text files. Compile Jv progrm. Crwl nd index the We. Red in dt stored in TOY input file formt. Automticlly crete Jv documenttion from Jvdoc comments. CAASCGGPYACGGWAGYHAGWH 5 6 Regulr Expressions: Bsic Opertions Regulr Expressions: Exmples Regulr expression. ottion to specify set of strings. Regulr expression. ottion is surprisingly expressive. opertion regulr expression mtches does not mtch regulr expression mtches does not mtch conctention every other string.*sp.* contins the trigrph sp rsperry crispred suspce suspecies wildcrd union closure.u.u.u. * cumulus jugulum succuus tumultuous every other string * (****)* multiple of three s.*0... fifth to lst digit is prentheses ( ) ()* every other string gcg(cgg gg)*ctg frgile X syndrome indictor gcgctg gcgcggctg gcgcggggctg gcgcgg cggcggcggctg gcgcggctg 7 8

3 Generlized Regulr Expressions Regulr Expressions in Jv Regulr expressions re stndrd progrmmer's tool. Built in to Jv, Perl, Unix, Python,. Additionl opertions typiclly dded for convenience. Ex: [-e]+ is shorthnd for ( c d e)( c d e)*. opertion regulr expression mtches does not mtch Vlidity checking. Is input in the set descried y the re? pulic clss Vlidte { pulic sttic void min(string[] rgs) { String re = rgs[0]; String input = rgs[1]; StdOut.println(input.mtches(re)); powerful string lirry method one or more chrcter clss (c)+de [A-Z-z][-z]* cde ccde lowercse Cpitlized de cde cmelcse 4illegl C 2 H 2 type zinc finger domin % jv Vlidte "C.{2,4C...[LIVMFYWC].{8H.{3,5H" CAASCGGPYACGGAAGYHAGAH true legl Jv identifier exctly k negtion [0-9]{5-[0-9]{4 [^eiou]{ rhythm decde % jv Vlidte "[$_A-Z-z][$_A-Z-z0-9]*" ident123 true vlid emil ddress (simplified) % jv Vlidte "[-z]+@([-z]+\.)+(edu com)" wyne@cs.princeton.edu true need quotes to "escpe" the shell 9 10 String Serching Methods String Serching Methods pulic clss String (Jv's String lirry) pulic clss String (Jv's String lirry) oolen mtches(string re) does this string mtch the given regulr expression oolen mtches(string re) does this string mtch the given regulr expression String replceall(string re, String str) replce ll occurrences of regulr expression with the replcement string String replceall(string re, String str) replce ll occurrences of regulr expression with the replcement string int indexof(string r, int from) return the index of the first occurrence of the string r fter the index from int indexof(string r, int from) return the index of the first occurrence of the string r fter the index from String[] split(string re) split the string round mtches of the given regulr expression String[] split(string re) split the string round mtches of the given regulr expression String s = StdIn.redAll(); s = s.replceall("\\s+", " "); replce ll sequences of whitespce chrcters with single spce String s = StdIn.redAll(); String[] words = s.split("\\s+"); crete rry of words in document regulr expression tht mtches ny whitespce chrcter 11 12

4 Solving the Pttern Mtch Prolem DFAs Regulr expressions re concise wy to descrie ptterns. How would you implement the method mtches()? Hrdwre: uild deterministic finite stte utomton (DFA). Softwre: simulte DFA. DFA: simple mchine tht solves pttern mtch prolem. Different mchine for ech pttern. Accepts or rejects string specified on input tpe. Focus on true or flse questions for simplicity. 14 Deterministic Finite Stte Automton (DFA) DFA nd RE Dulity Simple mchine with sttes. Begin in strt stte. Red first input symol. Move to new stte, depending on current stte nd input symol. Repet until lst input symol red. Accept input string if lst stte is leled Y. RE. Concise wy to descrie set of strings. DFA. Mchine to recognize whether given string is in given set. Dulity. For ny DFA, there exists RE tht descries the sme set of strings; for ny RE, there exists DFA tht recognizes the sme set. Y * (****)* DFA Y multiple of 3 's multiple of 3 's Input Prcticl consequence of dulity proof: to mtch RE, (i) uild DFA nd (ii) simulte DFA on input string

5 Implementing Pttern Mtcher Appliction: Hrvester Prolem. Given RE, crete progrm tht tests whether given input is in set of strings descried. Step 1. Build the DFA. A compiler! See COS 226 or COS 320. Step 2. Simulte it with given input. Hrvest informtion from input strem. Hrvest ptterns from DA. % jv Hrvester "gcg(cgg gg)*ctg" chromosomex.txt gcgcggcggcggcggcggctg gcgctg gcgctg gcgcggcggcggggcggggcggctg Stte stte = strt; while (!StdIn.isEmpty()) { chr c = StdIn.redChr(); stte = stte.next(c); StdOut.println(stte.ccept()); Hrvest emil ddresses from we for spm cmpign. % jv Hrvester "[-z]+@([-z]+\.)+(edu com)" rs@cs.princeton.edu mi@cs.princeton.edu doug@cs.princeton.edu wyne@cs.princeton.edu Appliction: Hrvester Hrvest informtion from input strem. Use Pttern dt type to compile regulr expression to FA. Use Mtcher dt type to simulte FA. import jv.util.regex.pttern; import jv.util.regex.mtcher; pulic clss Hrvester { pulic sttic void min(string[] rgs) { String re = rgs[0]; In in = new In(rgs[1]); String input = in.redall(); Pttern pttern = Pttern.compile(re); Mtcher mtcher = pttern.mtcher(input); look for next mtch while (mtcher.find()) { StdOut.println(mtcher.group()); the mtch most recently found equivlent, ut more efficient representtion of DFA crete FA from RE crete FA simultor Appliction: Prsing Dt File Ex: prsing n CBI genome dt file. LOCUS AC p DA liner HTG 13-OV-2003 DEFIITIO Ornithorhynchus ntinus clone CLM1-393H9, ACCESSIO AC VERSIO AC GI: KEYWORDS HTG; HTGS_PHASE2; HTGS_DRAFT. SOURCE Ornithorhynchus ntinus (pltypus) ORIGI 1 tgttttct ttgccgtgc tgttttttcc cggtttttc gtcggtgtt ggggccc 61 gtgttctgt ttgtttttg ctgccgt gctgctcgt gtctctgc tgcgct // comment 121 gccgcggg gtgcc gtttgtgtg ctgt gggctgt ttcttct ggtgcg ccccccgct tgtcgc ttctttgt tg line numers spces the DA heder info comments 19 20

6 Appliction: Prsing Dt File Regulr Expressions Ex: prsing n CBI genome dt file. String re = "[ ]*[0-9]+([ctg ]*).*"; Pttern pttern = Pttern.compile(re); In in = new In(filenme); while (!in.isempty()) { String line = in.redline(); Mtcher mtcher = pttern.mtcher(line); if (mtcher.find()) { String s = mtcher.group(1).replceall(" ", ""); // do something with s extrct the prt of mtch in prens LOCUS AC p DA liner HTG 13-OV-2003 DEFIITIO Ornithorhynchus ntinus clone CLM1-393H9, ACCESSIO AC VERSIO AC GI: KEYWORDS HTG; HTGS_PHASE2; HTGS_DRAFT. SOURCE Ornithorhynchus ntinus (pltypus) ORIGI 1 tgttttct ttgccgtgc tgttttttcc cggtttttc gtcggtgtt ggggccc 61 gtgttctgt ttgtttttg ctgccgt gctgctcgt gtctctgc tgcgct // comment 121 gccgcggg gtgcc gtttgtgtg ctgt gggctgt ttcttct ggtgcg ccccccgct tgtcgc ttctttgt tg Summry Fundmentl Questions Progrmmer. Regulr expressions re powerful pttern mtching tool. Implement regulr expressions with finite stte mchines. Theoreticin. RE is compct description of set of strings. DFA is n strct mchine tht solves RE pttern mtch prolem. You. Prcticl ppliction of core CS principles. Q. Are there ptterns tht cnnot e descried y ny RE/DFA? A. Yes. Bit strings with equl numer of 0s nd 1s. Deciml strings tht represent prime numers. DA strings tht re Wtson-Crick complemented plindromes. Q. Cn we extend RE/DFA to descrie richer ptterns? A. Yes. Context free grmmr (e.g., Jv). Turing mchines