Abstract—Interaction-based and state-based modeling are two complementary approaches of behavior modeling. The former focuses on global interactions between system components. The latter concentrates on the internal states of individual components. Both approaches have been proven useful in practice. One challenging and important research objective is to combine the modeling power of both effectively and then use the combination as the basis for automatic design synthesis. We present a combination of interaction-based and state-based modeling, namely, Live Sequence Charts and Z, for system specification. We then propose a way of generating distributed design from the combinations. Our approach handles systems with intensive interactive behaviors as well as complex state structures. Index Terms—Z language, live sequence charts, specification, synthesis. 1

All bisimulation problems for pushdown automata are at least PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACE-hard.

We consider the problem of simulation preorder/equivalence between infinitestate processes and finite-state ones. We prove that simulation preorder (in both directions) and simulation equivalence are intractable between all major classes of infinite-state systems and finite-state ones. This result is obtained by showing that the problem whether a BPA (or BPP) process simulates 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. The decidability border for the mentioned problem is also established. Simulation preorder (in both directions) and simulation equivalence are shown to be decidable in EXPTIME between pushdown processes and finite-state ones. On the other hand, simulation preorder is undecidable between PA and finite-state processes in both directions. The obtained results also hold for those PA and finite-state processes which are determini...

Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has non-elementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is co-NP-hard. Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31]. We improve this result by showing that weak bisimilarity of BPP is \Pi p 2 -hard. Finally, we show that the problems if a BPP is regular (i.e., finite) w.r.t. strong and weak bisimilarity are co-NP-hard and \Pi p 2 -hard, respectively.

We study the problem of strong/weak bisimilarity between processes of one-counter automata and \Thetanite-state processes. We show that the problem of weak bisimilarity between processes of one-counter nets (which are `weak' one-counter automata) and \Thetanite-state processes is DP-hard (in particular, it means that the problem is both NP and co-NP hard). The same technique is used to demonstrate co-NP- hardness of strong bisimilarity between processes of one-counter nets. Then we design an algorithm which decides weak bisimilarity between processes of one-counter automata and \Thetanite-state processes in time which is polynomial for most `practical' instances, giving a characterization of all hard instances as a byproduct. Moreover, we show how to ef\Thetaciently compute a rather tight bound for the time which is needed to solve a given instance. Finally, we prove that the problem of strong bisimilarity between processes of one-counter automata and \Thetanite-state pro...