Answers to Self-Study Questions

Test Yourself #1

Test Yourself #2

The regular expression

is the same as (digit | (letter letter)), and means "one digit, or two letters". The regular expression is the same as (digit | (letter (letter *))), and means "one digit, or one or more letters". The regular expression is the same as (digit | (letter *)), and means "one digit, or zero or more letters".

Test Yourself #3

Two new tokens, INT_LITERAL and DBL_LITERAL would be defined. The regular expressions for those tokens are

The finite-state machines are 

                                       --------
                                       |      |
INT_LITERAL                            v      | digit
                  -----   digit     =======   |
                  | S | ----------> ||   || ---
                  -----             =======


                                       ------
                                       |    |
DBL_LITERAL                         v    | digit
                  -----   digit     -----   |
                  | S | ----------> |   | ---
                  -----             -----              digit
                                       |         -----       =======
                                       --------> |   | ----> ||   ||<--
                                        dot      -----       =======  |
                                                                |     |
                                                                -------
                                                                 digit
The modified finite-state machines are 

                                 -----
                                 |   |
INT_LITERAL                      v   | digit
               -----   digit     -----                        ================
               | S | ----------> |   | ---------------------->|| put back    ||
               -----             ----- any char except digit  || 1 char;     ||
                                                              || return      ||
                                                              || INT_LITERAL ||
                                                              ================

                             digit         digit
                             ------         -----
                             |    |         |   |
DBL_LITERAL                  v    |         v   |                   =================
           -----   digit     -----          -----                   || put back    ||
           | S | ----------> |   | -------> |   | ----------------->|| 1 char;     ||
           -----             -----  dot     ----- any char except   || return      ||
                                                  digit             || DBL_LITERAL ||
                                                                    =================

The "combined" finite-state machine would be augmented by having one new edge out of the start state, leading to the node labeled A below. 

                      -----
                      |   |
                      v   | digit
    -----   digit     -----                        ================
    | A | ----------> |   | ---------------------->|| put back    ||
    -----             -----    any char except     || 1 char;     ||
                       |       digit or dot        || return      ||
                  dot  |                           || INT_LITERAL ||
                       v          digit            =================
                     -----        -----
                     |   |        |   |
                     -----        v   |
                       | digit    ----- any char except digit   ================
                       ---------> |   | ----------------------> || put back    ||
                                  -----                         || 1 char;     ||
                                                                || return      ||
                                                                || DBL_LITERAL ||
                                                                =================