License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2017.38
URN: urn:nbn:de:0030-drops-78049
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7804/
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Abdulla, Parosh Aziz ; Aiswarya, C. ; Atig, Mohamed Faouzi

Data Multi-Pushdown Automata

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LIPIcs-CONCUR-2017-38.pdf (0.7 MB)

Abstract

We extend the classical model of multi-pushdown systems by considering systems that operate on a finite set of variables ranging over natural numbers. The conditions on variables are defined via gap-order constraints that allow to compare variables for equality, or to check that the gap between the values of two variables exceeds a given natural number. Furthermore, each message inside a stack is equipped with a data item representing its value. When a message is pushed to the stack, its value may be defined by a variable. When a message is popped, its value may be copied to a variable. Thus, we obtain a system that is infinite in multiple dimensions, namely we have a number of stacks that may contain an unbounded number of messages each of which is equipped with a natural number.
It is well-known that the verification of any non-trivial property of multi-pushdown systems is undecidable, even for two stacks and for a finite data-domain. In this paper, we show the decidability of the reachability problem for the classes of data multi-pushdown system that admit a bounded split-width (or equivalently a bounded tree-width). As an immediate consequence, we obtain decidability for several subclasses of data multi-pushdown systems. These include systems with single stacks, restricted ordering policies on stack operations, bounded scope, bounded phase, and bounded context switches.

BibTeX - Entry

@InProceedings{abdulla_et_al:LIPIcs:2017:7804,
  author =	{Parosh Aziz Abdulla and C. Aiswarya and Mohamed Faouzi Atig},
  title =	{{Data Multi-Pushdown Automata}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Roland Meyer and Uwe Nestmann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7804},
  URN =		{urn:nbn:de:0030-drops-78049},
  doi =		{10.4230/LIPIcs.CONCUR.2017.38},
  annote =	{Keywords: Pushdown Systems, Model-Checking, Gap-Order, Bounded Split-Width}
}

Keywords: Pushdown Systems, Model-Checking, Gap-Order, Bounded Split-Width
Collection: 28th International Conference on Concurrency Theory (CONCUR 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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