English

Parameterized complexity results for 1-safe Petri nets

Logic in Computer Science 2011-06-13 v1 Computational Complexity Data Structures and Algorithms Formal Languages and Automata Theory

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

Cite

@article{arxiv.1106.2122,
  title  = {Parameterized complexity results for 1-safe Petri nets},
  author = {M. Praveen and Kamal Lodaya},
  journal= {arXiv preprint arXiv:1106.2122},
  year   = {2011}
}

Comments

Full version of the paper appearing in CONCUR 2011

R2 v1 2026-06-21T18:20:40.996Z