Deciding determinism of caterpillar expressions

Caterpillar expressions have been introduced by Brüggemann-Klein and Wood for applications in markup languages. Caterpillar expressions provide a convenient formalism for specifying the operation of tree-walking automata on unranked trees. Here we give a formal definition of determinism of caterpillar expressions that is based on the language of instruction sequences defined by the expression. We show that determinism of caterpillar expressions can be decided in polynomial time.