Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

The coverability and boundedness problems for Petri nets are known to be Expspace-complete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space O(ef(k,W)poly(n)), where ef(k,W) is some exponential function and poly(n) is some polynomial in the size of the input. We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.Comment: Full version of the paper appearing in IPEC 201

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

Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE

We consider concurrent systems that can be modelled as $1$-safe Petri nets communicating through a fixed set of buffers (modelled as unbounded places). We identify a parameter $ben$, which we call ``benefit depth\u27\u27, formed from the communication graph between the buffers. We show that for our system model, the coverability and boundedness problems can be solved in polynomial space assuming $ben$ to be a fixed parameter, that is, the space requirement is $f(ben)p(n)$, where $f$ is an exponential function and $p$ is a polynomial in the size of the input. We then obtain similar complexity bounds for modelchecking a logic based on such counting properties. This means that systems that have sparse communication patterns can be analyzed more efficiently than using previously known algorithms for general Petri nets