Friday, December 5, 2008

A breeze of fresh air: structural induction.

One of the reasons why I like CSC236 is that I absolutely adore induction techniques. It is then indescribable how fascinated and excited I was when Danny drew the curtains and showed us the third flavour of induction: structural induction!

It really seems nature to me that many things can be expressed using structural induction. Larger sets can be decomposed as smaller sets. Trees are a combination of trunks and branches. Society is hierarchical and each hierarchy can be divided into different levels of various importances. Structural inductions can thus be utilized to prove a wide range of problems. I didn’t really understand why Professor Danny referred structural induction as “half of an induction technique”, but so be it.

It has to be noted that structural induction plays a very important role in the several definitions of regular expressions and languages introduced later in the course. See, structural induction rocks!

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