A note on SE-systems and regular canonical systems

A synchronized extension system is a 4-tuple G = (V, L-1, L-2, S), where V is an alphabet and L-1, L-2 and S are languages over V. Such systems genera te languages extending L-1 by L-2 to the left or to the right, and synchron izing on words in S. In this note we consider the relationship between synchronized extension sy stems and regular canonical systems. We are able to give a simplified and g eneralized proof for the classical result concerning the regularity of the languages defined by regular canonical systems.