3 Search Results for "Katsumata, Shin-ya"

Document
DOI: 10.4230/LITES.8.2.3
Higher-Dimensional Timed and Hybrid Automata

Authors: Uli Fahrenberg

Published in: LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2

Abstract
We introduce a new formalism of higher-dimensional timed automata, based on Pratt and van Glabbeek’s higher-dimensional automata and Alur and Dill’s timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based algorithms. We also extend the setting to higher-dimensional hybrid automata.The interest of our formalism is in modeling systems which exhibit both real-time behavior and concurrency. Other existing formalisms for real-time modeling identify concurrency and interleaving, which, as we shall argue, is problematic.
Cite as

Uli Fahrenberg. Higher-Dimensional Timed and Hybrid Automata. In LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2, pp. 03:1-03:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@Article{fahrenberg:LITES.8.2.3,
  author =	{Fahrenberg, Uli},
  title =	{{Higher-Dimensional Timed and Hybrid Automata}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{03:1--03:16},
  ISSN =	{2199-2002},
  year =	{2022},
  volume =	{8},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.8.2.3},
  doi =		{10.4230/LITES.8.2.3},
  annote =	{Keywords: timed automaton, higher-dimensional automaton, precubical set, real time, non-interleaving concurrency, hybrid automaton}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.21
Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down

Authors: Mayuko Kori, Ichiro Hasuo, and Shin-ya Katsumata

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
The coincidence between initial algebras (IAs) and final coalgebras (FCs) is a phenomenon that underpins various important results in theoretical computer science. In this paper, we identify a general fibrational condition for the IA-FC coincidence, namely in the fiber over an initial algebra in the base category. Identifying (co)algebras in a fiber as (co)inductive predicates, our fibrational IA-FC coincidence allows one to use coinductive witnesses (such as invariants) for verifying inductive properties (such as liveness). Our general fibrational theory features the technical condition of stability of chain colimits; we extend the framework to the presence of a monadic effect, too, restricting to fibrations of complete lattice-valued predicates. Practical benefits of our categorical theory are exemplified by new "upside-down" witness notions for three verification problems: probabilistic liveness, and acceptance and model-checking with respect to bottom-up tree automata.
Cite as

Mayuko Kori, Ichiro Hasuo, and Shin-ya Katsumata. Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 21:1-21:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kori_et_al:LIPIcs.CONCUR.2021.21,
  author =	{Kori, Mayuko and Hasuo, Ichiro and Katsumata, Shin-ya},
  title =	{{Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.21},
  URN =		{urn:nbn:de:0030-drops-143982},
  doi =		{10.4230/LIPIcs.CONCUR.2021.21},
  annote =	{Keywords: initial algebra, final coalgebra, fibration, category theory}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.156
Codensity Liftings of Monads

Authors: Shin-ya Katsumata and Tetsuya Sato

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
We introduce a method to lift monads on the base category of a fibration to its total category using codensity monads. This method, called codensity lifting, is applicable to various fibrations which were not supported by the categorical >>-lifting. After introducing the codensity lifting, we illustrate some examples of codensity liftings of monads along the fibrations from the category of preorders, topological spaces and extended psuedometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We next study the liftings of algebraic operations to the codensity-lifted monads. We also give a characterisation of the class of liftings (along posetal fibrations with fibred small limits) as a limit of a certain large diagram.
Cite as

Shin-ya Katsumata and Tetsuya Sato. Codensity Liftings of Monads. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 156-170, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{katsumata_et_al:LIPIcs.CALCO.2015.156,
  author =	{Katsumata, Shin-ya and Sato, Tetsuya},
  title =	{{Codensity Liftings of Monads}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{156--170},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.156},
  URN =		{urn:nbn:de:0030-drops-55329},
  doi =		{10.4230/LIPIcs.CALCO.2015.156},
  annote =	{Keywords: Monads, Lifting, Fibration, Giry Monad}
}
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