For this purpose, we use the standard notation by which the restriction of a function f : X → Y to a subset A ⊆ X is written as: Transition systems that can be defined using composition of elementary transitions with restrictions are said to be divisible.
a stack-based transition system S = (C, T, c s , C t ) is divisible if and only if every transition in T is of the form a stack-based transition system is divisible if and only if each of its transitions can be written as a composition of restrictions of the elementary transitions SHIFT, UNSHIFT, REDUCE, LEFT-aRC, and RIGHT-aRC.