Ideal, theoretical computers are rather mathematical objects: they are, equivalently, algorithms, or effective procedures, or abstract automata, or functions which can be specified recursively, or formal languages. Things to learn more about: Classifications of machines and languages beyond the classical, fourlevel Chomsky hierarchy. Hierarchies of computational power. Abstractalgebraic treatment of automata. Effects of making automata stochastic. Techniques for proving equivalence of automata; of minimizing automata. Bisimulation. Techniques for inferring automata or grammars from their languages, especially when generation is stochastic. Nonfinitestate transducers. Stochastic contextfree grammars and their connections with branching processes. Logics of time and computation. Analog computation. What forms are structurally stable? Other forms of unconventional.

Website: http://cscs.umich.edu/~crshalizi/notebooks/computation.html