FORWARD ANALYSIS OF DYNAMIC NETWORK OF PUSHDOWN SYSTEMS IS EASIER WITHOUT ORDER

Abstract

Dynamic networks of Pushdown Systems (DNPS 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 yields decidability of the forward analysis of DNPS. Finally, we extend this result to the model where configurations are sets of threads running in parallel.