Bonds of Constrained Systems and Their Characteristics

A constrained system is a set of words satisfying some constraints on the appearance of subwords, and the study on constrained systems is the core of the study on constrained coding. The notion of constrained coding has been often applied in data storage media to reduce the likelihood of errors.Given data sequences satisfying some constraints, it is not always possible to directly concatenate the data sequences so that the resulting sequence also satisfies the constraints. In this paper, we define a bond to be a sequence that can concatenate any allowed data sequences without violating the constraints, and present a necessary and sufficient condition on the existence of a bond. We also discuss on the length of a bond and the complexity of finding a bond, together with some examples of bonds.