Mathematical definition of deterministic and non-deterministic random bit generators Can anyone give the mathematical definition of deterministic and non-deterministic random bit generator?

Providing a reference will also be very helpful.
Deterministic random bit generator is a function that takes as input a secret seed and possibly other inputs and produces (long) strings of output bits with the following property: for all adversaries with (polynomially) bounded computational power, the distribution of output bits is indistinguishable from a uniform, independent distribution of bits.

I don't think there is a strictly "mathematical" definition of true random bit source (I guess this is what you mean by 'non-deterministic') since it would need to define something that is now well captured by mathematics (external, physical source of entropy).

NIST in its standard SP800-90Ar1 defines non-deterministic random bit generator as:


  An RBG that always has access to an entropy source and (when working properly) produces output bitstrings that have full entropy. Often called a True Random Number (or Bit) Generator. (Contrast with a deterministic random bit generator).


A good reference book that covers the topic of randomness and random bit generators is "Random Number Generators - Principles and Practices".