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We consider the verification problem of a class of infinite-state systems called wPAD. These systems can be used to model programs with (possibly recursive) procedure calls and dynamic creation of parallel processes. They correspond to PAD models extended with an acyclic finite-state control unit, where PAD models can be seen as combinations of prefix rewrite systems (pushdown systems) with context-free multiset rewrite systems (synchronization-free Petri nets). Recently, we have presented symbolic reachability techniques for the class of PAD based on the use of a class of unranked tree automata. In this paper, we generalize our previous work to the class wPAD which is strictly larger than PAD. This generalization brings a positive answer to an open question on decidability of the model checking problem for wPAD against EF logic. Moreover, we show how symbolic reachability analysis of wPAD can be used in (under) approximate analysis of Synchronized PAD, a (Turing) powerful model for multithreaded programs (with unrestricted synchronization between parallel processes). This leads to a pragmatic approach for detecting the presence of erroneous behaviors in these models based on the bounded reachability paradigm where the notion of bound considered here is the number of synchronization actions.