Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
The mathematics of Petri nets
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
On the power of bounded concurrency I: finite automata
Journal of the ACM (JACM)
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Decidability and Complexity of Petri Net Problems - An Introduction
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
On the Complexity of the Linear-Time mu -calculus for Petri-Nets
ICATPN '97 Proceedings of the 18th International Conference on Application and Theory of Petri Nets
Describing parameterized complexity classes
Information and Computation
A parametric analysis of the state-explosion problem in model checking
Journal of Computer and System Sciences
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Does treewidth help in modal satisfiability?
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Parameterized Complexity
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We associate a graph with a 1-safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]-hardness results for many problems about 1-safe Petri nets. As a corollary, this proves a conjecture of Downey et. al. about the hardness of some graph pebbling problems. We consider the parameter benefit depth (that is known to be helpful in getting better algorithms for general Petri nets) and again give W[1]-hardness results for various problems on 1-safe Petri nets. We also consider the stronger parameter vertex cover number. Combining the well known automata-theoretic method and a powerful fixed parameter tractability (Fpt) result about Integer Linear Programming, we give a Fpt algorithm for model checking Monadic Second Order (MSO) formulas on 1-safe Petri nets, with parameters vertex cover number and the size of the formula.