The Last Stretch

I've now found that my optimism on heading into the last segment of the course was warranted. As I mentioned in my last post, despite some trouble with test 2, my grasp and enjoyment of formal languages, FSAs and further course material has been encouraging.

I think part of my enjoyment of this material comes from the difference in feel of reasoning about symbols and strings instead of simply numbers. Don't get me wrong, there is always an appeal to a precise proof in a more typical mathematical domain. But reasoning with language just seems refreshing.

Regex's, in their practical usage, have been a favourite of mine for some time. The theoretical variety of Regex's we studied in 236 is seemingly not so distant from the practical sort. This similarity really helped to engage me in the material.

When it comes to FSAs, I would almost say they have a certain graphical or mechanical appeal.
Reasoning using the machinery of an FSA is fun. I think it's fun in the sort of way a mechanical contraption is. The FSA graphical simulators available on the web, and demonstrated by Danny in lecture, only add to the more tangible aspect of FSAs.

Now, for the validation of my optimism. Assignment three and test three proved to be satisfying. They both involved a fair amount of effort, but I didn't feel too stumped, and enjoyed the level of challenge of both their sets of questions.

Specifically, I found the test to be quite fair. I'd like to discuss the question about proving that a Regex without a union operator denoted a language of length zero, one or infinity. Thinking about the implications of using each allowed operator, that is, concatenation and kleene star, on their own, along with looking at base cases for possible input strings gave me an intuition on how to structure my proof. This intuition came to pretty quickly after following this line of reasoning. Splitting the proof into cases of just concatenation being used, and then a case for using kleene star allowed me to delve into the language-length implications of either operator. And of course the implication of a blank regex on its denoted language's length seemed fairly trivial.

All in all, I'm happy with my experience with the last part of the course! Enjoyable material coupled with very reasonable work made it fun... relatively speaking, in terms of a university course.