A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants

Timed-Arc Petri Nets (TAPN) is a well studied extension of the classical Petri net model where tokens are decorated with real numbers that represent their age. Unlike reachability, which is known to be undecidable for TAPN, boundedness and coverability remain decidable. The model is supported by a recent tool called TAPAAL which, among others, further extends TAPN with invariants on places in order to model urgency. The decidability of boundedness and coverability for this extended model has not yet been considered. We present a reduction from two-counter Minsky machines to TAPN with invariants to show that both the boundedness and coverability problems are undecidable

Crystallisation and preliminary X-ray analysis of the receptor-binding domain of human and bovine α2-macroglobulin

AbstractThe receptor-binding domains (RBDs) of human and bovine α2-macroglobulin (α2M) have been isolated after limited proteolysis of methylamine-treated α2M with papain. Single crystals of the RBDs have been grown by vapour diffusion. Crystals of human RBD are very thin plates unsuited for data collection. However, crystals of RBD from bovine α2M give diffraction patterns suitable for X-ray analysis, and a complete dataset with a maximum resolution of 2.3 Å has been collected with synchrotron radiation at cryogenic temperature. The crystals belong to spacegroup P3121 or P3221 with cell parameters a = b = 106.8 Å, c = 72.2 Å