Lecture 10 Closure Properties of Regular Languages Topics: Extended RegExpr Thompson Construction Test 1 Post Mortem October 1, 2008 CSCE 355 Foundations of Computation

– 2 – CSCE 355 Fall 2008 Last Time: Readings 2.3 Mutual Induction Proof revisited Languages denoted by regular expressions Examples Ruby Regular Expressions TEST 1 – September 29 thNew: Readings section 3.1,3.2(skip DFA  RE), 3.3 Ruby Pickaxe Book Ruby: Matching in files

– 3 – CSCE 355 Fall 2008 Homework  English descriptions  Regular expressions 3.1.1b – The set of strings of 0’s and 1’s such that the tenth symbol from the right is a c - The set of strings of 0’s and 1’s with at most one pair of consecutive 1’s b The set of strings of 0’s and 1’s such that the number of zeroes is divisible by 5.  Regular expressions  English descriptions 3.14b (0*1*)*000(0+1)* 3.14c (0+10)*1*  Regular expressions  εNFA (Thompson construction) 3.2.4b (0+1) c 00(0+1)* 3.14b, 3.14c convert to εNFA  Text matching re for matching phone numbers (international etc)

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– 5 – CSCE 355 Fall 2008 Grep  Unix utility  man grep  man –k regexp

– 6 – CSCE 355 Fall 2008 Thompson Construction  Based on recursive (inductive) definition of regular expressions  We describe NFAs (with epsilon moves) that recognize the base cases.  Then assuming we have NFAs for smaller expressions r and s we construct NFAs for r + s rs r*

– 7 – CSCE 355 Fall 2008 Thompson Construction Examples  rs, r | s, r*

– 8 – CSCE 355 Fall 2008 Thompson Construction Examples  Extended regular expressions

– 9 – CSCE 355 Fall 2008 Lex and Flex  Regular definitions  Pattern match  “.” Last pattern  Examples digit = [0-9] alpha= [a-zA-Z_] id = {alpha} ({alpha} | {letter} | ‘_’)* % id {install_InSymbolTable(yytext); return(ID);} while { return (KEYWHILE);}

– 10 – CSCE 355 Fall 2008 Compilation

– 11 – CSCE 355 Fall 2008 DFA  RegExpr  NFA  DFA  Regular Languages

– 12 – CSCE 355 Fall 2008 Algebraic Laws for Regular Expressions  What does it mean re,=re2 ?  E?

– 13 – CSCE 355 Fall 2008 Languages are Sets So Properties are Inherited  AUB = BUA so r l s = s l r r l s = s l r

– 14 – CSCE 355 Fall 2008 Associativity

– 15 – CSCE 355 Fall 2008 Commutivity

– 16 – CSCE 355 Fall 2008 Annihilator for concatenation  Identity  annihilator

– 17 – CSCE 355 Fall 2008 Checking for Equality of Two Regular Expressions  s = r ?  (r+s)* = r* s*

– 18 – CSCE 355 Fall 2008 Is L intersection R regular?

– 19 – CSCE 355 Fall 2008 Is the Complement of a Regular Lang. regular?

– 20 – CSCE 355 Fall 2008 Not all Languages are regular

– 21 – CSCE 355 Fall 2008 Pumping Lemma

– 22 – CSCE 355 Fall 2008 Every finite language is Regular

– 23 – CSCE 355 Fall 2008 Test Post Mortem

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