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

't Hooft Anomaly Matching for Discrete Symmetries

We show how to extend the 't Hooft anomaly matching conditions to discrete symmetries. We check these discrete anomaly matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N=1 supersymmetric Yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N=1 supersymmetric theories based on exceptional groups.Comment: 6 pages, LaTeX. Talk presented by Csaba Csaki at the XXXIIIrd Rencontres de Moriond, Electroweak Interactions and Unified Theories, Les Arcs, Savoie, France, March 14-21, 199

Geometrically protected triple-point crossings in an optical lattice

We show how to realize topologically protected crossings of three energy bands, integer-spin analogs of Weyl fermions, in three-dimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated and leads to isolated triple-point crossings (TPCs) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the type-II, or tilted, TPC. Our Rapid Communication shows that spin-1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.Comment: 5 pages, 2 figures + 3 pages, 3 figures supplemental material. Added appendix on model symmetries, fixed typos and added references. This is the final, published versio