Reachability in Vector Addition Systems is Primitive-Recursive in Fixed Dimension

The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known upper bound on this problem is not primitive-recursive, even when considering systems of fixed dimension. We provide significant refinements to the classical decomposition algorithm of Mayr, Kosaraju, and Lambert and to its termination proof, which yield an ACKERMANN upper bound in the general case, and primitive-recursive upper bounds in fixed dimension. While this does not match the currently best known TOWER lower bound for reachability, it is optimal for related problems

KReach : a tool for reachability in petri nets

We present KReach, a tool for deciding reachability in general Petri nets. The tool is a full implementation of Kosaraju’s original 1982 decision procedure for reachability in VASS. We believe this to be the first implementation of its kind. We include a comprehensive suite of libraries for development with Vector Addition Systems (with States) in the Haskell programming language. KReach serves as a practical tool, and acts as an effective teaching aid for the theory behind the algorithm. Preliminary tests suggest that there are some classes of Petri nets for which we can quickly show unreachability. In particular, using KReach for coverability problems, by reduction to reachability, is competitive even against state-of-the-art coverability checkers

The dynamics and control of large flexible space structures-IV

The effects of solar radiation pressure as the main environmental disturbance torque were incorporated into the model of the rigid orbiting shallow shell and computer simulation results indicate that within the linear range the rigid modal amplitudes are excited in proportion to the area to mass ratio. The effect of higher order terms in the gravity-gradient torque expressions previously neglected was evaluated and found to be negligible for the size structures under consideration. A graph theory approach was employed for calculating the eigenvalues of a large flexible system by reducing the system (stiffness) matrix to lower ordered submatrices. The related reachability matrix and term rank concepts are used to verify controllability and can be more effective than the alternate numerical rank tests. Control laws were developed for the shape and orientation control of the orbiting flexible shallow shell and numerical results presented