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We consider the problem of simulation preorder/equivalence between infinite-state process and finite-state ones. First, we describe a general method how to utilize the decidability of bisimulation problems to solve (certain instances of) the corresponding simulation problems. For certain process classes, the method allows us to design effective reductions of simulation problems to their bisimulation counterparts and some new decidability border for the problem of simulation preorder/equivalence are decidable in EXPTIME between pushdown and finite-state ones. On the other hand, simulation preorder is undecidable between PA and finite-state process in both directions. These results also hold for those PA and finite-state process which are deterministic and normed, and trace equivalence is also shown to be undecidable for PA. Finally, we prove that simulation preorder (in both directions) and simulation equivalence are interact able between all classes of infinite-state systems (in the hierarchy of process rewrite systems) and finite-state ones. This result is obtained by showing that the problem whether a BPA (or BPP) process simulation a finite-state one is PSPACE- hard and the other direction is co-NP-hard; consequently, simulation equivalence between BPA (or BPP) and finite-state processes is also co-NP-hard.