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[Apprentice123]

What the automaton generated by language: ((a(ab)^*)b)^* ?

[fayyazlodhi]

Theory of automata isn't very fresh in mind (6+ years ago) though i used to be good at solving state machines. Any way i assume task is to reduce the above language to a final result.

Here is my poor attempt that i have serious doubts about being any where near true. Still i thought of giving a try

((a(ab)^*)b)^* // original one -
it results in a2b (read as "a square b")

a2b ^ * // Taking exclusive or with a square b of * (any thing) would basically result in inverting bits of a2b.

~a2b // Because exclusive or inverts all bits of a number

(~a2b) b // b should be removed from ~ because it's bit is turned on by multiplication
(~a2)

Finally ~a2 ^ * (again exclusive OR with * should return in ~)
so ~(~a2)

results in a2.




~a2 ^ *
a2