What is a general feedback register? What is a linear feedback register? Give an example of a general feedback register which is not a linear feedback register and prove that it has the stated property.

By giving proofs or counterexamples, establish which, if any, of the following statements are true and which, if any, are false.

(i) Given two linear feedback registers, there always exist non-zero initial fills for which the outputs are identical.

(ii) If two linear feedback registers have different lengths, there do not exist non-zero initial fills for which the outputs are identical.

(iii) If two linear feedback registers have different lengths, there exist non-zero initial fills for which the outputs are not identical.

(iv) There exist two linear feedback registers of different lengths and non-zero initial fills for which the outputs are identical.