What is mutual induction and how does that differ from regular induction? http://web.cecs.pdx.edu/~black/CS311/proof_by_mutual_induction.pdf
I read this and I fail to see any difference. It's the same thing, prove for n = 0 and then prove for n = k+1.

Mutual induction is the most accurate way for proving L=L(A), 'L' being the language and "L(A)" being the language of a given automaton.  The reason for this, is because you need to mutually prove that a certain string will transit through a certain state by a certain input and that transition depends on previous states.  In other words, this method of proof clearly convinces that a certain language is accepted by the automaton by proving that a set of states will mutually lead to a final state by a given string.
