Divisibility and State Complexity

Abstract

It is well known that the set of all natural numbers divisible by a fixed modulus m can be recognized by a finite state machine, assuming that the numbers are written in standard base-B representation. It is much harder to determine the state complexity of the minimal recognizer [1]. In this article we discuss the size of minimal recognizers for a variety of numeration systems, including reverse base-B representation and the Fibonacci system.