Generalizing the Asymmetric Run-length-limited Systems

Fori= 1,2, ifXiis a synchronized system generated byVi={viαi:αiviαi∈ B(Xi),αi6⊆vi}whereαiis a synchronizing word forXi, then a natural generalization of an asymmetric-RLL(d1, k1, d0, k0)systems is a coded systemZgenerated by{v1α1v2α2:viαi∈Vi,i= 1,2}.We investigate the dynamical properties ofZ. We show thatZis sofic or has specification withvariable gap length (SVGL) if and only ifX1andX2are so. Also, ifZis SFT or AFT, thenXandYare SFT or AFT respectively and sufficient conditions for the converse will be given.