Pushdown Tree Automata, Algebraic Tree Systems, and Algebraic Tree Series

Branching Pushdown Tree Automata

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 push-move views its matching pops as an unbounded, unorde...

Algebraic Systems and Pushdown Automata

Nonlinear Tree Pattern Pushdown Automata

A new kind of an acyclic pushdown automaton for an ordered tree is presented. The nonlinear tree pattern pushdown automaton represents a complete index of the tree for nonlinear tree patterns and accepts all nonlinear tree patterns which match the tree. Given a tree with n nodes, the number of such nonlinear tree patterns is O((2+ v)n), where v is the number of variables in the patterns. We dis...

Ordered Tree-Pushdown Systems

We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an applicati...

Tree Automata for Analyzing Dynamic Pushdown Networks

Dynamic Pushdown Networks (DPNs) are an abstract model for concurrent programs with recursive procedures and dynamic process creation. Usually, DPNs are described with an interleaving semantics, where an execution is a sequence of steps. Recently, we introduced a true-concurrency semantics for DPNs, where executions are trees. The standard analysis methods for DPNs are based on a saturation alg...