Searching Short Recurrences of Nonlinear Shift Registers via Directed Acyclic Graphs

Finding a recurrence of a shift register gives its equivalent shift register in Fibonacci configuration and hence helps to decide whether different nonlinear shift registers are equivalent, i.e., whether they generate the same set of output sequences. We define a dependence graph of a shift register and it is a directed acyclic graph related to the shift register. We show that existence of a dependence graph with a special property of a nonlinear shift register ensures existence of a short recurrence of the sequence generated by the nonlinear shift register. We also present an algorithm to search dependence graphs of a nonlinear shift register.