 
Summary: Branching Pushdown Tree Automata
Rajeev Alur and Swarat Chaudhuri
University of Pennsylvania
Abstract. We observe that pushdown tree automata (PTAs) known in
the literature cannot express combinations of branching and pushdown
properties. This is because a PTA processes the children of a tree node
in possibly different control states but with identical stacks. We propose
branching pushdown tree automata (BPTAs) as a solution. In a BPTA,
a pushmove views its matching pops as an unbounded, unordered set of
successor moves and can assert existential and universal requirements on
them, just the way finite automata on unranked, unordered trees pass
requirements to the children of a tree node. We show that BPTAs can
express some natural properties and are more expressive than PTAs.
Using a smallmodel theorem, we prove their emptiness problem to be
decidable. The problem becomes undecidable, however, if pushmoves
are allowed to specify the ordering of matching pops.
1 Introduction
Regular languages of trees [1] have been studied extensively in the literature [10]
and found a number of applications. Automata accepting such languages can
reason about paths in a tree existentially ("a symbol a is seen along some path
