Abstract
A word is called Petri net solvable if it is isomorphic to the reachability graph of an unlabelled Petri net. In this paper, the class of finite, two-letter, Petri net solvable words is studied. A linear time, necessary condition allows for an educated guess at which words are solvable and which are not. A full decision procedure with a time complexity of \(O(n^2)\) can be built based on letter counting. The procedure is fully constructive and can either yield a Petri net solving a given word or determine why this fails. Algorithms solving the same problem based on systems of integer inequalities reflecting the potential Petri net structure are only known to be in \(O(n^3)\). Finally, the decision procedure can be adapted from finite to cyclic words.
This research has been supported by DFG (German Research Foundation) through grants Be 1267/15-1 ARS (Algorithms for Reengineering and Synthesis), Be 1267/14-1 CAVER (Comparative Analysis and Verification for Correctness-Critical Systems), and Graduiertenkolleg GRK-1765 SCARE (System Correctness under Adverse Conditions).
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Acknowledgments
We would like to thank Raymond Devillers for his very helpful suggestions to improve this paper and Valentin Spreckels for his valuable support in computing the experimental data.
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Best, E., Erofeev, E., Schlachter, U., Wimmel, H. (2016). Characterising Petri Net Solvable Binary Words. In: Kordon, F., Moldt, D. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2016. Lecture Notes in Computer Science(), vol 9698. Springer, Cham. https://doi.org/10.1007/978-3-319-39086-4_4
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DOI: https://doi.org/10.1007/978-3-319-39086-4_4
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