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DOI: 10.4230/LIPIcs.FSTTCS.2018.44
URN: urn:nbn:de:0030-drops-99432
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9943/
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Penelle, Vincent ; Salvati, Sylvain ; Sutre, Grégoire

On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems

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Abstract

Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach à la Karp and Miller can still be used to solve termination and boundedness. We provide a decidable characterisation of runs that can be iterated arbitrarily many times, which is the main ingredient of Karp and Miller's approach. However, the resulting Karp and Miller procedure only gives a semi-algorithm for HOPVASS. In fact, we show that coverability, termination and boundedness are all undecidable for HOPVASS, even in the restricted subcase of one counter and an order 2 stack. On the bright side, we prove that this semi-algorithm is in fact an algorithm for higher-order pushdown automata.

BibTeX - Entry

@InProceedings{penelle_et_al:LIPIcs:2018:9943,
  author =	{Vincent Penelle and Sylvain Salvati and Gr{\'e}goire Sutre},
  title =	{{On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{44:1--44:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9943},
  URN =		{urn:nbn:de:0030-drops-99432},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.44},
  annote =	{Keywords: Higher-order pushdown automata, Vector addition systems, Boundedness problem, Termination problem, Coverability problem}
}

Keywords: Higher-order pushdown automata, Vector addition systems, Boundedness problem, Termination problem, Coverability problem
Seminar: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 23.11.2018


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