Undulations

JARGON ALERT: This post is related to Computation Theory, and anyone but Computer Scientists or Engineers (or budding ones) might find this crap.

Formal Languages and Automata Theory - FLAT in short - is what our paper on Computation Theory, Automata and Language Theory called; a core paper for our Computer Engineer course. Automata and theoretical computer science were fields that used to interest me from when I was a high-school student (that was when I first read about the halting problem), and it still does - however, I found the paper less than extremely appealing - it was good and rather easy to handle, but somewhere lacking the elegance.

When I started to think why, I was asymptotically approaching a possible answer - the lack of a proper axiomatic approach. The entire science is infested with a lot of conjectures, lemmas, models and theorems, many of them fundamental and clever in their own respect - however, most of the arguments and proofs where rather tangled, with a lot of obscure number theoretic and inductive arguments involved. Does this point to the lack of an axiomatic base to the entire field?

While recursion is elementary to language and automata theory, and recursion and induction a straightforward way to approach things, this can’t be no reason that there cannot be an axiomatic approach to the science, building up on some basic axioms, and constructing further proofs and dijectures upon these, without needing to resort to contorted verbal arguments or qualitative descriptions. Could this be possible?

I really hope this is possible and might probably pursue this very aspect as my term-end project; axiomatizing the field of theoretical computer science. If I succeed, that would be the achievement of my life as a computer scientist. Thoughts?