Universal Computation is 'Almost Surely' Chaotic

Details Universal Computation is 'Almost Surely' Chaotic Universal Computation is 'Almost Surely' Chaotic

2011-11-21

arxiv.org/abs/1111.4949v1

Computer Science

Computational Complexity

Scientific paper

Some fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as Turing Machines operate in integer num- ber space, the standard notions of a chaotic system is not immediately applicable for it. Changing the state space of the Turing Machine from integer to rational numbers set, the condition for chaotic dynamics can be established, as presented in the current paper. Further it is deduced that, for random input almost all computation performed by an Universal Turing Machine would be chaotic.

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