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Documents authored by Zantema, Hans

Document
DOI: 10.4230/LIPIcs.RTA.2015.160
Proving non-termination by finite automata

Authors: Jörg Endrullis and Hans Zantema

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic.
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Jörg Endrullis and Hans Zantema. Proving non-termination by finite automata. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 160-176, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{endrullis_et_al:LIPIcs.RTA.2015.160,
  author =	{Endrullis, J\"{o}rg and Zantema, Hans},
  title =	{{Proving non-termination by finite automata}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{160--176},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.160},
  URN =		{urn:nbn:de:0030-drops-51952},
  doi =		{10.4230/LIPIcs.RTA.2015.160},
  annote =	{Keywords: non-termination, finite automata, regular languages}
}
Document
DOI: 10.4230/LIPIcs.RTA.2015.285
Transforming Cycle Rewriting into String Rewriting

Authors: David Sabel and Hans Zantema

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract
We present new techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. We present three such transformations, and prove for all of them that they are sound and complete. Apart from this transformational approach, we extend the use of matrix interpretations as was studied before. We present several experiments showing that often our new techniques succeed where earlier techniques fail.
Cite as

David Sabel and Hans Zantema. Transforming Cycle Rewriting into String Rewriting. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 285-300, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{sabel_et_al:LIPIcs.RTA.2015.285,
  author =	{Sabel, David and Zantema, Hans},
  title =	{{Transforming Cycle Rewriting into String Rewriting}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{285--300},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.285},
  URN =		{urn:nbn:de:0030-drops-52032},
  doi =		{10.4230/LIPIcs.RTA.2015.285},
  annote =	{Keywords: rewriting systems, string rewriting, termination}
}
Document
DOI: 10.4230/LIPIcs.RTA.2012.240
Triangulation in Rewriting

Authors: Vincent van Oostrom and Hans Zantema

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012)

Abstract
We introduce a process, dubbed triangulation, turning any rewrite relation into a confluent one. It is more direct than usual completion, in the sense that objects connected by a peak are directly related rather than their normal forms. We investigate conditions under which this process preserves desirable properties such as termination.
Cite as

Vincent van Oostrom and Hans Zantema. Triangulation in Rewriting. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 240-255, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{vanoostrom_et_al:LIPIcs.RTA.2012.240,
  author =	{van Oostrom, Vincent and Zantema, Hans},
  title =	{{Triangulation in Rewriting}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12)},
  pages =	{240--255},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.240},
  URN =		{urn:nbn:de:0030-drops-34964},
  doi =		{10.4230/LIPIcs.RTA.2012.240},
  annote =	{Keywords: triangulation,codeterminism,completion,(co)confluence,(co)termination}
}
Document
DOI: 10.4230/LIPIcs.RTA.2011.393
Proving Equality of Streams Automatically

Authors: Hans Zantema and Joerg Endrullis

Published in: LIPIcs, Volume 10, 22nd International Conference on Rewriting Techniques and Applications (RTA'11) (2011)

Abstract
Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. In this paper we focus on equality of streams, more precisely, for a given set of equations two stream terms are said to be equal if they are equal in every model satisfying the given equations. We investigate techniques for proving equality of streams suitable for automation. Apart from techniques that were already available in the tool CIRC from Lucanu and Rosu, we also exploit well-definedness of streams, typically proved by proving productivity. Moreover, our approach does not restrict to behavioral input format and does not require termination. We present a tool Streambox that can prove equality of a wide range of examples fully automatically.
Cite as

Hans Zantema and Joerg Endrullis. Proving Equality of Streams Automatically. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 393-408, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{zantema_et_al:LIPIcs.RTA.2011.393,
  author =	{Zantema, Hans and Endrullis, Joerg},
  title =	{{Proving Equality of Streams Automatically}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{393--408},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-30-9},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{10},
  editor =	{Schmidt-Schauss, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2011.393},
  URN =		{urn:nbn:de:0030-drops-31381},
  doi =		{10.4230/LIPIcs.RTA.2011.393},
  annote =	{Keywords: streams}
}
Document
DOI: 10.4230/LIPIcs.RTA.2010.401
Proving Productivity in Infinite Data Structures

Authors: Hans Zantema and Matthias Raffelsieper

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)

Abstract
For a general class of infinite data structures including streams, binary trees, and the combination of finite and infinite lists, we investigate the notion of productivity. This generalizes stream productivity. We develop a general technique to prove productivity based on proving context-sensitive termination, by which the power of present termination tools can be exploited. In order to treat cases where the approach does not apply directly, we develop transformations extending the power of the basic approach. We present a tool combining these ingredients that can prove productivity of a wide range of examples fully automatically.
Cite as

Hans Zantema and Matthias Raffelsieper. Proving Productivity in Infinite Data Structures. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 401-416, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{zantema_et_al:LIPIcs.RTA.2010.401,
  author =	{Zantema, Hans and Raffelsieper, Matthias},
  title =	{{Proving Productivity in Infinite Data Structures}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{401--416},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.401},
  URN =		{urn:nbn:de:0030-drops-26661},
  doi =		{10.4230/LIPIcs.RTA.2010.401},
  annote =	{Keywords: Productivity, infinite data structures, streams}
}
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