
432 Appendix A
6. Let C and D be regular expressions over some alphabet Σ. Show that the equation R = C +
RD is satisfied for an RE R = CD*. Draw a state diagram of a skeleton FSM showing this
relationship.
7. Let Σ = {0, 1} be the alphabet. Develop an FSM M
1
recognizing the language L
1
= {x ∈ Σ*
| x begins with 00 or 11}. Also develop another FSM M
2
recognizing the language
L
2
= {x ∈ Σ* | x ends with 00 or 11}. Could M
1
and M
2
be created out of an FSM accepting the
language {00, 11}? If yes, show how it can be done, if No, then prove it.
8. In some programming languages, identifiers may have embedded underscore ‘_’ characters.
However ...