Synchronized extension systems

Abstract.

Synchronized extension systems (SE-systems, for short) are 4-tuples $G=(V,L_1,L_2,S)$, where V is an alphabet and $L_1$, $L_2$ and S are languages overV. They generate languages extending $L_1$ by $L_2$ to the left or to the right, and synchronizing on words in S. Such systems appear naturally when considering stacks, queues, grammar-like generative devices, splicing systems, zigzag-codes etc.