Why is it said that if we know few bits of pseudo random sequence we can predict the whole of it? I am new to this cryptography and in the source from which i study it is said that if we know the first few bits of a pseudo random sequence we can predict the whole of it.How is it possible?
The source:http://www.youtube.com/watch?v=NjedHm04ETM
move to 7min 40sec and this is the source.
All psuedo random generators keep some limited state to calculate the next number in the sequence. you can think of it like a function $\delta(S)= \{output, S'\}$ with $S$ the internal state of the generator and represented by a finite number of bits.

This means that the number of states is limited (though it can be very big: a standard mersenne twister holds 2500 bytes of state)

As such if you get $n$ bytes of output with $n$ is larger than the number of bytes in the state then you can reasonably predict the current state of the output given enough time.

Note that if you group 256 bytes of output together and pass it though a sha-256 then it will take a very long time for you to restore first the original output of the generator and then the state when you know only the hash output. This is exactly how a secure PRNG works.