Forward Analysis of Dynamic Network of Pushdown Systems Is Easier without Order

Dynamic networks of Pushdown Systems (PDN in short) have been introduced to perform static analysis of concurrent programs that may spawn threads dynamically. In this model the set of successors of a regular set of configurations can be non-regular, making forward analysis of these models difficult. We refine the model by adding the associative-commutative properties of parallel composition, and we define Presburger weighted tree automata, an extension of weighted automata and tree automata, that accept the set of successors of a regular set of configurations. This allows forward analysis of PDN since these automata have a decidable emptiness problem and are closed under intersection.

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