We propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the shortest accepting run, and by proving a new pumping lemma for languages of 2-VASS. The technique is expected to be useful for settling questions concerning languages of 2-VASS, e.g., for establishing decidability status of the regular separability problem.
@InProceedings{czerwinski_et_al:LIPIcs.MFCS.2019.62, author = {Czerwi\'{n}ski, Wojciech and Lasota, S{\l}awomir and L\"{o}ding, Christof and Pi\'{o}rkowski, Rados{\l}aw}, title = {{New Pumping Technique for 2-Dimensional VASS}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {62:1--62:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.62}, URN = {urn:nbn:de:0030-drops-110066}, doi = {10.4230/LIPIcs.MFCS.2019.62}, annote = {Keywords: vector addition systems with states, pumping, decidability} }
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