Further Results on Pure Summing Registers and Complementary Ones
This work provides a complete understanding of the cycle structure for PSRs and CSRs, which is important for researchers working with these types of registers.
This paper completely determines the cycle structure of pure summing registers (PSR) and complementary summing registers (CSR). It also presents an algorithm to generate de Bruijn cycles from CSRs, inspired by prior work.
We decide completely the cycle structure of pure summing register (PSR) and complementary summing register (CSR). Based on the state diagram of CSR, we derive an algorithm to generate de Bruijn cycles from CSR inspired by Tuvi Etzion's publication in 1984. We then point out the limitation in generalizations of extended representation we use in the algorithm proposed, with a proof of the fact that only PSR and CSR contain pure cycles all dividing n+1.