Generating two differnet pseudorandom numbers using the same seed

Question

Is it possible to generate two different psuedorandom numbers on two separate program runs without using time as the seed? i.e. using the same seed on both runs, is it possible to get two different numbers?

Answer 1

In general, it is not possible to get different pseudorandom numbers using the same seed.

Pseudorandom numbers are, by definition, not truly random numbers and therefore are not composed from sources of entropy. Or, if the numbers do contain some entropy input, the input is not enough to cause the sequence to qualify as statistically "random." (An example of a property that such a sequence should have is runs of 1-bits n-bits-long with probability of 2^(-n), among many other properties of statistical randomness. The definition of statistical randomness becomes more sophisticated (in a sense, more "actual" or close to nature) as mathematics around randomness improves. This is another way of saying that, at any given time, the definitions of statistical randomness are about to become out-dated or obsolete.)

In any case, the vast majority of pseudorandom number generators are, in fact, completely deterministic.

The canonical¹ example of a pseudorandom number generator is a linear feedback shift register (LFSR). The LFSR can be implemented as a digital logic circuit containing a register which holds N bits, some gates numbering M, much less than N (e.g., M=1, M=2), usually these are XOR gates, which "feed back" into the register's bits at certain "tap bits." There is a lot about this on the web.

Given the same seed input, the LFSR will always generate the same sequence.

It is possible, using Walsh-Hadamard matrices, or otherwise called "M matrices", additionally called "sequency transform", to sample the output of an LFSR and determine that the sequence is, in fact, from an LFSR and also the structure of its gates and taps, as well as the current register content. From this information all sequence values are known, and it is possible to reverse out the possible seed values which were used as input. For these reasons, LFSRs are not suitable for security purposes such as random tokens for authentication.

1. By canonical, I am refering to Don Knuth's use of the LFSR as an example, as well as the timeless tradition which has ensued therefrom.

Answer 2

Not sure if you want to generate 2 different random numbers from same seed - or avoid it! But, if you really do want that, then similar to LFSRs, LCGs (Linear Congruential Generators) are often used to generate deterministic psuedo random numbers. You can 'easily' create 2 simple LCGs using different constants, which will generate 2 different psuedo random numbers for the same seed.