McMillan has recently proposed a new technique to avoid the state explosion problem in the verification of systems modelled with finite-state Petri nets. The technique requires to construct a finite initial part of the unfolding of the net. McMillan's algorithm for this task may yield initial parts that are larger than necessary (exponentially larger in the worst case). We present a refinement of the algorithm which overcomes this problem.
We investigate the notion of fair testing, a formal testing theory in the style of De Nicola and Hennessy, where divergences are disregarded as long as there axe visible outgoing transitions. The usual testing theories, such as the standard model of failure pre-order, do not allow such fair interpretations because of the way in which they ensure their compositionality with respect to abstraction from observable actions. This feature is usually present in the form of a hiding-operator (CSP, ACP, LOTOS) or part of parallel composition (CCS). Its application can introduce new divergences causing semantic complications. In this paper we present a testing scenario that captures the intended notion of fairness and induces a pre-congruence for abstraction. In the presence of a sufficiently strong synchronisation feature it is shown to be the coarsest pre-congruence contained in the (non-congruent) fair version of failure preorder. We also give a denotational characterisation.
In this paper, we develop a general technique for truncating Petri net unfoldings, parameterised according to the level of information about the original unfolding one wants to preserve. Moreover, we propose a new notion of completeness of a truncated unfolding. A key aspect of our approach is an algorithm-independent notion of cutoff events, used to truncate a Petri net unfolding. Such a notion is based on a cutting context and results in the unique canonical prefix of the unfolding. Canonical prefixes are complete in the new, stronger sense, and we provide necessary and sufficient conditions for its finiteness, as well as upper bounds on its size in certain cases. A surprising result is that after suitable generalisation, the standard unfolding algorithm presented in , and the parallel unfolding algorithm proposed in , despite being non-deterministic, generate the canonical prefix. This gives an alternative correctness proof for the former algorithm, and a new (much simpler) proof for the latter one.
This paper provides new insight into the connection between the trace-based lower part of van Glabbeek's linear-time, branching-time spectrum and its simulation-based upper part. We establish that ready simulation is fully abstract with respect to failures inclusion, when adding the conjunction operator that was proposed by the authors in [TCS 373(1-2):19-40] to the standard setting of labelled transition systems with (CSP-style) parallel composition. More precisely, we actually prove a stronger result by considering a coarser relation than failures inclusion, namely a preorder that relates processes with respect to inconsistencies that may arise under conjunctive composition. Ready simulation is also shown to satisfy standard logic properties and thus commends itself for studying mixed operational and logic languages.
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