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Documents authored by Nishida, Naoki


Document
Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems

Authors: Naoki Nishida and Yuya Maeda

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)


Abstract
A narrowing tree for a constructor term rewriting system and a pair of terms is a finite representation for the space of all possible innermost-narrowing derivations that start with the pair and end with non-narrowable terms. Narrowing trees have grammar representations that can be considered regular tree grammars. Innermost narrowing is a counterpart of constructor-based rewriting, and thus, narrowing trees can be used in analyzing constructor-based rewriting to normal forms. In this paper, using grammar representations, we extend narrowing trees to syntactically deterministic conditional term rewriting systems that are constructor systems. We show that narrowing trees are useful to prove two properties of a normal conditional term rewriting system: one is infeasibility of conditional critical pairs and the other is quasi-reducibility.

Cite as

Naoki Nishida and Yuya Maeda. Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 26:1-26:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{nishida_et_al:LIPIcs.FSCD.2018.26,
  author =	{Nishida, Naoki and Maeda, Yuya},
  title =	{{Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{26:1--26:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.26},
  URN =		{urn:nbn:de:0030-drops-91964},
  doi =		{10.4230/LIPIcs.FSCD.2018.26},
  annote =	{Keywords: conditional term rewriting, innermost narrowing, regular tree grammar}
}
Document
Confluence Competition 2018

Authors: Takahito Aoto, Makoto Hamana, Nao Hirokawa, Aart Middeldorp, Julian Nagele, Naoki Nishida, Kiraku Shintani, and Harald Zankl

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)


Abstract
We report on the 2018 edition of the Confluence Competition, a competition of software tools that aim to (dis)prove confluence and related properties of rewrite systems automatically.

Cite as

Takahito Aoto, Makoto Hamana, Nao Hirokawa, Aart Middeldorp, Julian Nagele, Naoki Nishida, Kiraku Shintani, and Harald Zankl. Confluence Competition 2018. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 32:1-32:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{aoto_et_al:LIPIcs.FSCD.2018.32,
  author =	{Aoto, Takahito and Hamana, Makoto and Hirokawa, Nao and Middeldorp, Aart and Nagele, Julian and Nishida, Naoki and Shintani, Kiraku and Zankl, Harald},
  title =	{{Confluence Competition 2018}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{32:1--32:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.32},
  URN =		{urn:nbn:de:0030-drops-92023},
  doi =		{10.4230/LIPIcs.FSCD.2018.32},
  annote =	{Keywords: Confluence, competition, rewrite systems}
}
Document
Reversible Term Rewriting

Authors: Naoki Nishida, Adrián Palacios, and Germán Vidal

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)


Abstract
Essentially, in a reversible programming language, for each forward computation step from state S to state S', there exists a constructive and deterministic method to go backwards from state S' to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or quantum computing, to name a few. In this paper, we focus on term rewriting, a computation model that underlies most rule-based programming languages. In general, term rewriting is not reversible, even for injective functions; namely, given a rewrite step t1 -> t2, we do not always have a decidable and deterministic method to get t1 from t2. Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define a transformation to make a rewrite system reversible using standard term rewriting.

Cite as

Naoki Nishida, Adrián Palacios, and Germán Vidal. Reversible Term Rewriting. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 28:1-28:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{nishida_et_al:LIPIcs.FSCD.2016.28,
  author =	{Nishida, Naoki and Palacios, Adri\'{a}n and Vidal, Germ\'{a}n},
  title =	{{Reversible Term Rewriting}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.28},
  URN =		{urn:nbn:de:0030-drops-59841},
  doi =		{10.4230/LIPIcs.FSCD.2016.28},
  annote =	{Keywords: term rewriting, reversible computation, program transformation}
}
Document
Complete Volume
OASIcs, Volume 46, WPTE'15, Complete Volume

Authors: Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß

Published in: OASIcs, Volume 46, 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)


Abstract
OASIcs, Volume 46, WPTE'15, Complete Volume

Cite as

Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß. OASIcs, Volume 46, WPTE'15, Complete Volume. In 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015). Open Access Series in Informatics (OASIcs), Volume 46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)


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@Proceedings{chiba_et_al:OASIcs.WPTE.2015,
  title =	{{OASIcs, Volume 46, WPTE'15, Complete Volume}},
  booktitle =	{2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-94-1},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{46},
  editor =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2015},
  URN =		{urn:nbn:de:0030-drops-52644},
  doi =		{10.4230/OASIcs.WPTE.2015},
  annote =	{Keywords: Conference proceedings, Concurrent Programming, Formal Definitions and Theory, Specifying and Verifying and Reasoning about Programs, Semantics of Programming Languages, Mathematical Logic, Grammars and Other Rewriting Systems, Deduction and Theorem Proving}
}
Document
Front Matter
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß

Published in: OASIcs, Volume 46, 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)


Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization

Cite as

Yuki Chiba, Santiago Escobar, Naoki Nishida, David Sabel, and Manfred Schmidt-Schauß. Frontmatter, Table of Contents, Preface, Workshop Organization. In 2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015). Open Access Series in Informatics (OASIcs), Volume 46, pp. i-xvi, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)


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@InProceedings{chiba_et_al:OASIcs.WPTE.2015.i,
  author =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{2nd International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2015)},
  pages =	{i--xvi},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-94-1},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{46},
  editor =	{Chiba, Yuki and Escobar, Santiago and Nishida, Naoki and Sabel, David and Schmidt-Schau{\ss}, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2015.i},
  URN =		{urn:nbn:de:0030-drops-51765},
  doi =		{10.4230/OASIcs.WPTE.2015.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
Document
Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems

Authors: Karl Gmeiner and Naoki Nishida

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)


Abstract
Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past. In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches.

Cite as

Karl Gmeiner and Naoki Nishida. Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 3-14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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@InProceedings{gmeiner_et_al:OASIcs.WPTE.2014.3,
  author =	{Gmeiner, Karl and Nishida, Naoki},
  title =	{{Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{3--14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.3},
  URN =		{urn:nbn:de:0030-drops-45871},
  doi =		{10.4230/OASIcs.WPTE.2014.3},
  annote =	{Keywords: conditional term rewriting, unraveling, condition elimination}
}
Document
Inverse Unfold Problem and Its Heuristic Solving

Authors: Masanori Nagashima, Tomofumi Kato, Masahiko Sakai, and Naoki Nishida

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)


Abstract
Unfold/fold transformations have been widely studied in various programming paradigms and are used in program transformations, theorem proving, and so on. This paper, by using an example, show that restoring an one-step unfolding is not easy, i.e., a challenging task, since some rules used by unfolding may be lost. We formalize this problem by regarding one-step program transformation as a relation. Next we discuss some issues on a specific framework, called pure-constructor systems, which constitute a subclass of conditional term rewriting systems. We show that the inverse of T preserves rewrite relations if T preserves rewrite relations and the signature. We propose a heuristic procedure to solve the problem, and show its successful examples. We improve the procedure, and show examples for which the improvement takes effect.

Cite as

Masanori Nagashima, Tomofumi Kato, Masahiko Sakai, and Naoki Nishida. Inverse Unfold Problem and Its Heuristic Solving. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 27-38, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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@InProceedings{nagashima_et_al:OASIcs.WPTE.2014.27,
  author =	{Nagashima, Masanori and Kato, Tomofumi and Sakai, Masahiko and Nishida, Naoki},
  title =	{{Inverse Unfold Problem and Its Heuristic Solving}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{27--38},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.27},
  URN =		{urn:nbn:de:0030-drops-45848},
  doi =		{10.4230/OASIcs.WPTE.2014.27},
  annote =	{Keywords: program transformation, unfolding, conditional term rewriting system}
}
Document
On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings

Authors: Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)


Abstract
In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs.

Cite as

Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner. On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 39-50, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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@InProceedings{nishida_et_al:OASIcs.WPTE.2014.39,
  author =	{Nishida, Naoki and Yanagisawa, Makishi and Gmeiner, Karl},
  title =	{{On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{39--50},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.39},
  URN =		{urn:nbn:de:0030-drops-45850},
  doi =		{10.4230/OASIcs.WPTE.2014.39},
  annote =	{Keywords: conditional term rewriting, unraveling, condition elimination}
}
Document
Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Authors: Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe

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


Abstract
Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature. They are not sound for every CTRS w.r.t. reduction, while they are complete w.r.t. reduction. Here, soundness w.r.t. reduction means that every reduction sequence of the corresponding unraveled TRS, of which the initial and end terms are over the original signature, can be simulated by the reduction of the original CTRS. In this paper, we show that an optimized variant of Ohlebusch's unraveling for deterministic CTRSs is sound w.r.t. reduction if the corresponding unraveled TRSs are left-linear or both right-linear and non-erasing. We also show that soundness of the variant implies that of Ohlebusch's unraveling.

Cite as

Naoki Nishida, Masahiko Sakai, and Toshiki Sakabe. Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 267-282, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)


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@InProceedings{nishida_et_al:LIPIcs.RTA.2011.267,
  author =	{Nishida, Naoki and Sakai, Masahiko and Sakabe, Toshiki},
  title =	{{Soundness of Unravelings for Deterministic Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{267--282},
  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.2011.267},
  URN =		{urn:nbn:de:0030-drops-31244},
  doi =		{10.4230/LIPIcs.RTA.2011.267},
  annote =	{Keywords: conditional term rewriting, program transformation}
}
Document
Program Inversion for Tail Recursive Functions

Authors: Naoki Nishida and German Vidal

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


Abstract
Program inversion is a fundamental problem that has been addressed in many different programming settings and applications. In the context of term rewriting, several methods already exist for computing the inverse of an injective function. These methods, however, usually return non-terminating inverted functions when the considered function is tail recursive. In this paper, we propose a direct and intuitive approach to the inversion of tail recursive functions. Our new technique is able to produce good results even without the use of an additional post-processing of determinization or completion. Moreover, when combined with a traditional approach to program inversion, it constitutes a promising approach to define a general method for program inversion. Our experimental results confirm that the new technique compares well with previous approaches.

Cite as

Naoki Nishida and German Vidal. Program Inversion for Tail Recursive Functions. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 283-298, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)


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@InProceedings{nishida_et_al:LIPIcs.RTA.2011.283,
  author =	{Nishida, Naoki and Vidal, German},
  title =	{{Program Inversion for Tail Recursive Functions}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{283--298},
  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.2011.283},
  URN =		{urn:nbn:de:0030-drops-31253},
  doi =		{10.4230/LIPIcs.RTA.2011.283},
  annote =	{Keywords: term rewriting, program transformation, termination}
}
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