The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known results. The paper also contains two decidability results. One concerns the Petri nets which are deterministic up to bisimilarity, the other concerns semilinear bisimulations and extends the result of [4] for Basic Parallel Processes. 1 Introduction The topic of the paper belongs to an interesting area in the theory of parallelism and concurrency, namely to the area of decidability questions for behavioural equivalences in various classes of (models of) processes. These questions are among the rst ones to ask when developing automated verication methods, for example. There is a large amount of equivalences in the literature (cf. e.g. [9]), nevertheless some of them are felt to be mor...

Abstract. We study the complexity of comparing pushdown automata (PDA) and context-free processes (BPA) to finite-state systems, w.r.t. strong and weak simulation preorder/equivalence and strong and weak bisimulation equivalence. We present a complete picture of the complexity of all these problems. In particular, we show that strong and weak simulation preorder (and hence simulation equivalence) is EXPTIME-complete between PDA/BPA and finite-state systems in both directions. For PDA the lower bound even holds if the finite-state system is fixed, while simulation-checking between BPA and any fixed finitestate system is already polynomial. Furthermore, we show that weak (and strong) bisimilarity between PDA and finite-state systems is PSPACE-complete, while strong (and weak) bisimilarity between two PDAs is EXPTIME-hard. 1

In [26], we investigated decidability issues for standard language equivalence for process description languages with two generalisations based on traditional approaches for capturing non-interleaving behaviour: pomset equivalence reflecting global causal dependency, and location equivalence reflecting spatial distribution of events. In this paper, we continue...

We show that checking weak bisimulation equivalence of two contextfree processes (also called BPA-processes) is EXPTIME-hard, even under the condition that the processes are normed. Furthermore, checking weak regularity (finiteness up to weak bisimilarity) for contextfree processes is EXPTIME-hard as well.

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