Re: Parsing Roman numbers

Check out K. John Gough, "Syntax Analysis and Software Tools"
(Addison-Wesley). He gives an example of a FSA for R(1..9), the roman
numerals 1 to 9, including the alternative for 4. He shows the sparse
state transition table you get, and uses this as a motivation for
compaction. A recognizer for the language from page 33 follows:


procedure RDIGIT (var valid:Boolean):
const error = 10; (* state 10 is error state*)
var state : 0..10;
        ch : char;


begin
  read(ch);
  state := 0;
  while ch in ['I','V','X'] do begin
    case state of
      0: case ch of
              'I': state := 1;
              'V': state := 5;
              'X': state := error;
            end;
      1: case ch of
              'I': state := 2;
              'V': state := 5;
              'X': state := 9;
            end;
      2: if ch = 'I' then state := 3 else state := error;
      5: if ch = 'I' then state := 6 else state := error;
      6: if ch = 'I' then state := 7 else state := error;
      7: if ch = 'I' then state := 8 else state := error;
      3,4,8,9,10 state := error;
    end; (* case *)
    read(ch);
  end (* while *);
  valid := state in [1..9];
end;




Typos are mine.


--
Debora Weber-Wulff dww@inf.fu-berlin.de
Institut fuer Informatik +49 30 89691 124
Nestorstr. 8-9
D-W-1000 Berlin 31
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