On the reachability analysis of acyclic networks of pushdown systems

We address the reachability problem in acyclic networks of pushdown systems. We consider communication based either on shared memory or on message passing through unbounded lossy channels. We prove mainly that the reachability problem between recognizable sets of configurations (i.e., definable by a finite union of products of finite-state automata) is decidable for such networks, and that for lossy channel pushdown networks, the channel language is effectively recognizable. This fact holds although the set of reachable configurations (including stack contents) for a network of depth (at least) 2 is not rational in general (i.e., not definable by a multi-tape finite automaton). Moreover, we prove that for a network of depth 1, the reachability set is rational and effectively constructible (under an additional condition on the topology for lossy channel networks).