Cellular Automata are Generic

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192

The physical Church-Turing thesis and non deterministic computation over the real numbers

On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where magnitudes are represented by real numbers

The physical Church thesis as an explanation of the Galileo thesis

The Galileo thesis is a consequence of the physical Church thesis

DOI 10.1007/s11047-011-9301-x The physical Church thesis as an explanation of the Galileo thesis

Abstract The Galileo thesis is a consequence of the physical Church thesis