Wed 07 Oct 2009
Due: Wed 14 Oct 2009
where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.
For all proofs of non-regularity, you should use the Pumping Lemma and/or appeal to closure properties. For examples of complete and correct Pumping Lemma proofs, see Examples 1.73, 1.74, 1.75, 1.76, and 1.77 on pages 80-82 of the Sipser text. See also the following handout.
The use of closure properties may also be helpful and may, in fact, yield complete proofs without the need to resort to the Pumping Lemma (as discussed in class).
For examples of proofs for non-regularity via closure properties and the Pumping Lemma, please see the following handout.
Required: 5 of the following 7 problems
Points: 20 pts per problem
Hint: For part (a), consider all strings in the language B in lexicographic order; write down the first dozen or so such strings. What properties do these strings have in common? Now construct a FA or RE for this language.
Hint: For part (a), consider the language
F' = F intersect ab*c*
appealing to closure properties and the Pumping Lemma.