CONCUR 2011: CONCUR 2011 – Concurrency Theory pp 358-372

# Parameterized Complexity Results for 1-safe Petri Nets

• M. Praveen
• Kamal Lodaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)

## Abstract

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.

## Keywords

Model Check Vertex Cover Linear Temporal Logic Primal Graph Path Decomposition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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