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Documents authored by Asada, Kazuyuki

Document
DOI: 10.4230/LIPIcs.FSCD.2026.34
Stabilized Profunctors and Matrix Representation

Authors: Takeshi Tsukada, Kazuyuki Asada, and Kengo Hirata

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
The (bi)category of profunctors on groupoids is a categorification of the relational model of linear logic. Its objects are not just sets but rather sets whose elements are equipped with groups encoding their symmetries, and its morphisms carry actions by these symmetries. While detailed information on such symmetries helps with, e.g., adequacy proofs of profunctorial models, it makes operations such as composition more difficult to compute. A way to ease the computation is to transform a profunctor into a matrix. Although the matrix representation is not functorial in general, it is known to behave well for certain subclasses, such as the class of profunctors definable by λ-terms. The mathematical reason behind this phenomenon, however, was not understood. This paper shows that the key is stability. Stability is a classical concept in domain theory, and has been extended to profunctors in Taylor’s work and further developed by Fiore et al. All λ-definable profunctors are known to be stabilized, and we show that the matrix representation behaves well for stabilized profunctors. We prove that the matrix representation defines a functor from stabilized profunctors to matrices that preserves the linear logic structures.
Cite as

Takeshi Tsukada, Kazuyuki Asada, and Kengo Hirata. Stabilized Profunctors and Matrix Representation. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{tsukada_et_al:LIPIcs.FSCD.2026.34,
  author =	{Tsukada, Takeshi and Asada, Kazuyuki and Hirata, Kengo},
  title =	{{Stabilized Profunctors and Matrix Representation}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.34},
  URN =		{urn:nbn:de:0030-drops-263847},
  doi =		{10.4230/LIPIcs.FSCD.2026.34},
  annote =	{Keywords: Profunctor, weighted relational model, stability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.21
On Average-Case Hardness of Higher-Order Model Checking

Authors: Yoshiki Nakamura, Kazuyuki Asada, Naoki Kobayashi, Ryoma Sin'ya, and Takeshi Tsukada

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We study a mixture between the average case and worst case complexities of higher-order model checking, the problem of deciding whether the tree generated by a given λ Y-term (or equivalently, a higher-order recursion scheme) satisfies the property expressed by a given tree automaton. Higher-order model checking has recently been studied extensively in the context of higher-order program verification. Although the worst-case complexity of the problem is k-EXPTIME complete for order-k terms, various higher-order model checkers have been developed that run efficiently for typical inputs, and program verification tools have been constructed on top of them. One may, therefore, hope that higher-order model checking can be solved efficiently in the average case, despite the worst-case complexity. We provide a negative result, by showing that, under certain assumptions, for almost every term, the higher-order model checking problem specialized for the term is k-EXPTIME hard with respect to the size of automata. The proof is based on a novel intersection type system that characterizes terms that do not contain any useless subterms.
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Yoshiki Nakamura, Kazuyuki Asada, Naoki Kobayashi, Ryoma Sin'ya, and Takeshi Tsukada. On Average-Case Hardness of Higher-Order Model Checking. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nakamura_et_al:LIPIcs.FSCD.2020.21,
  author =	{Nakamura, Yoshiki and Asada, Kazuyuki and Kobayashi, Naoki and Sin'ya, Ryoma and Tsukada, Takeshi},
  title =	{{On Average-Case Hardness of Higher-Order Model Checking}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.21},
  URN =		{urn:nbn:de:0030-drops-123439},
  doi =		{10.4230/LIPIcs.FSCD.2020.21},
  annote =	{Keywords: Higher-order model checking, average-case complexity, intersection type system}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.22
Size-Preserving Translations from Order-(n+1) Word Grammars to Order-n Tree Grammars

Authors: Kazuyuki Asada and Naoki Kobayashi

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
Higher-order grammars have recently been studied actively in the context of automated verification of higher-order programs. Asada and Kobayashi have previously shown that, for any order-(n+1) word grammar, there exists an order-n grammar whose frontier language coincides with the language generated by the word grammar. Their translation, however, blows up the size of the grammar, which inhibited complexity-preserving reductions from decision problems on word grammars to those on tree grammars. In this paper, we present a new translation from order-(n+1) word grammars to order-n tree grammars that is size-preserving in the sense that the size of the output tree grammar is polynomial in the size of an input tree grammar. The new translation and its correctness proof are arguably much simpler than the previous translation and proof.
Cite as

Kazuyuki Asada and Naoki Kobayashi. Size-Preserving Translations from Order-(n+1) Word Grammars to Order-n Tree Grammars. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{asada_et_al:LIPIcs.FSCD.2020.22,
  author =	{Asada, Kazuyuki and Kobayashi, Naoki},
  title =	{{Size-Preserving Translations from Order-(n+1) Word Grammars to Order-n Tree Grammars}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.22},
  URN =		{urn:nbn:de:0030-drops-123440},
  doi =		{10.4230/LIPIcs.FSCD.2020.22},
  annote =	{Keywords: higher-order grammar, word language, tree language, complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.14
Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered

Authors: Kazuyuki Asada and Naoki Kobayashi

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
Asada and Kobayashi [ICALP 2017] conjectured a higher-order version of Kruskal's tree theorem, and proved a pumping lemma for higher-order languages modulo the conjecture. The conjecture has been proved up to order-2, which implies that Asada and Kobayashi's pumping lemma holds for order-2 tree languages, but remains open for order-3 or higher. In this paper, we prove a variation of the conjecture for order-3. This is sufficient for proving that a variation of the pumping lemma holds for order-3 tree languages (equivalently, for order-4 word languages).
Cite as

Kazuyuki Asada and Naoki Kobayashi. Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{asada_et_al:LIPIcs.FSTTCS.2018.14,
  author =	{Asada, Kazuyuki and Kobayashi, Naoki},
  title =	{{Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.14},
  URN =		{urn:nbn:de:0030-drops-99138},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.14},
  annote =	{Keywords: higher-order grammar, pumping lemma, Kruskal's tree theorem, well-quasi-ordering, simply-typed lambda calculus}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.97
Pumping Lemma for Higher-order Languages

Authors: Kazuyuki Asada and Naoki Kobayashi

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages.
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Kazuyuki Asada and Naoki Kobayashi. Pumping Lemma for Higher-order Languages. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{asada_et_al:LIPIcs.ICALP.2017.97,
  author =	{Asada, Kazuyuki and Kobayashi, Naoki},
  title =	{{Pumping Lemma for Higher-order Languages}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{97:1--97:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.97},
  URN =		{urn:nbn:de:0030-drops-74323},
  doi =		{10.4230/LIPIcs.ICALP.2017.97},
  annote =	{Keywords: pumping lemma, higher-order grammars, Kruskal's tree theorem}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.111
On Word and Frontier Languages of Unsafe Higher-Order Grammars

Authors: Kazuyuki Asada and Naoki Kobayashi

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Higher-order grammars are an extension of regular and context-free grammars, where nonterminals may take parameters. They have been extensively studied in 1980's, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result.
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Kazuyuki Asada and Naoki Kobayashi. On Word and Frontier Languages of Unsafe Higher-Order Grammars. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 111:1-111:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{asada_et_al:LIPIcs.ICALP.2016.111,
  author =	{Asada, Kazuyuki and Kobayashi, Naoki},
  title =	{{On Word and Frontier Languages of Unsafe Higher-Order Grammars}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{111:1--111:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.111},
  URN =		{urn:nbn:de:0030-drops-62469},
  doi =		{10.4230/LIPIcs.ICALP.2016.111},
  annote =	{Keywords: intersection types, higher-order grammars}
}
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