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Other Issues - § 3.9 – Not Discussed

Other Issues - § 3.9 – Not Discussed. More advanced algorithm construction – regular expression to DFA directly. space required. time to simulate. NFA. O(|r|). O(|r|*|x|). DFA. O(2 |r| ). O(|x|). Final Notes : R.E. to NFA Construction.

brennan-stephenson
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Other Issues - § 3.9 – Not Discussed

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  1. Other Issues - § 3.9 – Not Discussed • More advanced algorithm construction – regular expression to DFA directly

  2. space required time to simulate NFA O(|r|) O(|r|*|x|) DFA O(2|r|) O(|x|) Final Notes : R.E. to NFA Construction • So, an NFA may be simulated by algorithm, when NFA is constructed using Previous techniques • Algorithm run time is proportional to |N| * |x| where |N| is the number of states and |x| is the length of input • Alternatively, we can construct DFA from NFA and use the resulting Dtran to recognize input: where |r| is the length of the regular expression.

  3. Pulling Together Concepts • Designing Lexical Analyzer Generator • Reg. Expr.  NFA construction • NFA  DFA conversion • DFA simulation for lexical analyzer • Recall Lex Structure • Pattern Action • Pattern Action • … … • Each pattern recognizes lexemes • Each pattern described by regular expression (a | b)*abb  e.g.  (abc)*ab  etc. Recognizer!

  4. Lex Specification  Lexical Analyzer • Let P1, P2, … , Pn be Lex patterns • (regular expressions for valid tokens in prog. lang.) • Construct N(P1), N(P2), … N(Pn) • Note: accepting state of N(Pi) will be marked by Pi • Construct NFA: N(P1) • Lex applies conversion algorithm to construct DFA that is equivalent!   N(P2)  N(Pn)

  5. Lex Specification Lex Compiler Transition Table (a) Lex Compiler FA Simulator Transition Table Pictorially lexeme input buffer (b) Schematic lexical analyzer

  6. NFA’s : start a 1 2 start a b b 3 4 5 6 a b start 7 8 b Example P1 : aP2 : abbP3 : a*b+ 3 patterns P1 P2 P3

  7. 1 0 Example – continued (2) Combined NFA :  a P1 2  a b b start P2 3 4 5 6 a b  P3 7 8 b Examples a a b a {0,1,3,7} {2,4,7} {7} {8} deathpattern matched: - P1 - P3 - a b b {0,1,3,7} {2,4,7} {5,8} {6,8}pattern matched: - P1P3P2,P3 break tie in favor of P2

  8. Input Symbol STATE a b Pattern {0,1,3,7} {2,4,7} {8} none {2,4,7} {7} {5,8} P1 {8} - {8} P3 {7} {7} {8} none {5,8} - {6,8} P3 {6,8} - {8} P2 Example – continued (3) Alternatively Construct DFA: (keep track of correspondence between patterns and new accepting states) break tie in favor of P2

  9. Minimizing the Number of States of DFA • Construct initial partition  of S with two groups: accepting/ non-accepting. • (Construct new)For each group G of  do begin • Partition G into subgroups such that two states s,tof G are in the same subgroup iff for all symbols astates s,t have transitions on a to states of the same group of . • Replace G in new by the set of all these subgroups. • Compare new and . If equal, final:=  then proceed to 4, else set  :=new and goto 2. • Aggregate states belonging in the groups of final

  10. example a a A a F B a b b a D C b b b a a A,C,D B,F b Minimized DFA: b

  11. Using LEX Lex Program Structure: declarations%%translation rules%%auxiliary procedures Name the file e.g. test.lexThen, “lex test.lex”produces the file“lex.yy.c” (a C-program)

  12. LEX %{ /* definitions of all constants LT, LE, EQ, NE, GT, GE, IF, THEN, ELSE, ... */ %} ...... letter [A-Za-z] digit [0-9] id {letter}({letter}|{digit})* ...... %% if { return(IF);} then { return(THEN);} {id} { yylval = install_id(); return(ID); } ...... %% install_id() { /* procedure to install the lexeme to the ST */ C declarations declarations Rules Auxiliary

  13. Example of a Lex Program int num_lines = 0, num_chars = 0; %% \n {++num_lines; ++num_chars;}. {++num_chars;} %% main( argc, argv )int argc; char **argv; { ++argv, --argc; /* skip over program name */ if ( argc > 0 ) yyin = fopen( argv[0], "r" ); else yyin = stdin; yylex(); printf( "# of lines = %d, # of chars = %d\n", num_lines, num_chars ); }

  14. Another Example %{ #include <stdio.h> %} WS [ \t\n]* %% [0123456789]+ printf("NUMBER\n"); [a-zA-Z][a-zA-Z0-9]* printf("WORD\n"); {WS} /* do nothing */ . printf(“UNKNOWN\n“); %% main( argc, argv ) int argc; char **argv; { ++argv, --argc; if ( argc > 0 ) yyin = fopen( argv[0], "r" ); else yyin = stdin; yylex(); }

  15. Concluding Remarks • Focused on Lexical Analysis Process, Including • - Regular Expressions • Finite Automaton • Conversion • Lex • Interplay among all these various aspects of lexical analysis Looking Ahead: • The next step in the compilation process is Parsing: • Top-down vs. Bottom-up • - Relationship to Language Theory

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