The principle was originally stated by Deutsch with respect to finitary machines and processes. He observed that classical physics, which makes use of the concept of real numbers, cannot be simulated by a Turing machine, which can only represent computable reals.
- Quantum complexity theory
- Digital physics
- Holographic principle and Bekenstein bound, which prohibit unlimited precision real numbers in the physical universe
- Nielsen, Michael. "Interesting problems: The Church–Turing–Deutsch Principle". Retrieved 10 May 2014.
- Deutsch, D. (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer" (PDF). Proceedings of the Royal Society. London. 400: 97–117. doi:10.1098/rspa.1985.0070.
- Deutsch, D. (1997). "6: Universality and the Limits of Computation". The Fabric of Reality. New York: Allan Lane. ISBN 0-14-027541-X.
- Christopher G. Timpson Quantum Computers: the Church-Turing Hypothesis Versus the Turing Principle in Christof Teuscher, Douglas Hofstadter (eds.) Alan Turing: life and legacy of a great thinker, Springer, 2004, ISBN 3-540-20020-7, pp. 213–240