Rules: Individual work only. Because theory is abstract, there a generally many variations in concrete answers to problems; if I see strangely similar answers, I'll be pretty suspicious!

The problems: Taken from the end of the chapter.

# 1, 4,
#6 a,c (+ be sure to explain your reasoning well)
#12 (+ give concise explanation of why your grammar works)
#16 (+ be sure to include a concise argument as how your grammar works. Hint: the set can be seen as union of two subsets: strings where aa preceeds bb and strings where the opposite is true. Think about making a grammar for each and then combining them...)
#20 (+ again, clear argument/construction of your grammar)
#30 (hint: prove that prefixes of ANY sentential form must have at least as many a's as b's. Hint hint hint: recursion)

To hand in: A very clean and readable write-up. The "Standards for Homework" posted on the web page apply to your work in this class. As theoretical work often involves lots of pondering and erasing I recommend that you (a) work in pencil and (b) use scratch paper to figure it out, then write up the final version neatly.