25 Search Results for "Milius, Stefan"

Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2023.21
On Kripke, Vietoris and Hausdorff Polynomial Functors ((Co)algebraic pearls)

Authors: Jiří Adámek, Stefan Milius, and Lawrence S. Moss

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor V on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from V, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgebras and we deduce that they also have initial algebras. We present an analogous class of endofunctors on the category of extended metric spaces, using in lieu of V the Hausdorff functor ℋ. We prove that the ensuing Hausdorff polynomial functors have terminal coalgebras and initial algebras. Whereas the canonical constructions of terminal coalgebras for Vietoris polynomial functors takes ω steps, one needs ω + ω steps in general for Hausdorff ones. We also give a new proof that the closed set functor on metric spaces has no fixed points.
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Jiří Adámek, Stefan Milius, and Lawrence S. Moss. On Kripke, Vietoris and Hausdorff Polynomial Functors ((Co)algebraic pearls). In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{adamek_et_al:LIPIcs.CALCO.2023.21,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Milius, Stefan and Moss, Lawrence S.},
  title =	{{On Kripke, Vietoris and Hausdorff Polynomial Functors}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.21},
  URN =		{urn:nbn:de:0030-drops-188189},
  doi =		{10.4230/LIPIcs.CALCO.2023.21},
  annote =	{Keywords: Hausdorff functor, Vietoris functor, initial algebra, terminal coalgebra}
}
Document
Early Ideas
DOI: 10.4230/LIPIcs.CALCO.2023.24
Higher-Order Mathematical Operational Semantics (Early Ideas)

Authors: Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
We present a higher-order extension of Turi and Plotkin’s abstract GSOS framework that retains the key feature of the latter: for every language whose operational rules are represented by a higher-order GSOS law, strong bisimilarity on the canonical operational model is a congruence with respect to the operations of the language. We further extend this result to weak (bi-)similarity, for which a categorical account of Howe’s method is developed. It encompasses, for instance, Abramsky’s classical compositionality theorem for applicative similarity in the untyped λ-calculus. In addition, we give first steps of a theory of logical relations at the level of higher-order abstract GSOS.
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Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat. Higher-Order Mathematical Operational Semantics (Early Ideas). In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 24:1-24:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goncharov_et_al:LIPIcs.CALCO.2023.24,
  author =	{Goncharov, Sergey and Milius, Stefan and Schr\"{o}der, Lutz and Tsampas, Stelios and Urbat, Henning},
  title =	{{Higher-Order Mathematical Operational Semantics}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{24:1--24:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.24},
  URN =		{urn:nbn:de:0030-drops-188213},
  doi =		{10.4230/LIPIcs.CALCO.2023.24},
  annote =	{Keywords: Abstract GSOS, lambda-calculus, applicative bisimilarity, bialgebra}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.48
Positive Data Languages

Authors: Florian Frank, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Positive data languages are languages over an infinite alphabet closed under possibly non-injective renamings of data values. Informally, they model properties of data words expressible by assertions about equality, but not inequality, of data values occurring in the word. We investigate the class of positive data languages recognizable by nondeterministic orbit-finite nominal automata, an abstract form of register automata introduced by Bojańczyk, Klin, and Lasota. As our main contribution we provide a number of equivalent characterizations of that class in terms of positive register automata, monadic second-order logic with positive equality tests, and finitely presentable nondeterministic automata in the categories of nominal renaming sets and of presheaves over finite sets.
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Florian Frank, Stefan Milius, and Henning Urbat. Positive Data Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{frank_et_al:LIPIcs.MFCS.2023.48,
  author =	{Frank, Florian and Milius, Stefan and Urbat, Henning},
  title =	{{Positive Data Languages}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.48},
  URN =		{urn:nbn:de:0030-drops-185828},
  doi =		{10.4230/LIPIcs.MFCS.2023.48},
  annote =	{Keywords: Data Languages, Register Automata, MSO, Nominal Sets, Presheaves}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.114
Nominal Topology for Data Languages

Authors: Fabian Birkmann, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We propose a novel topological perspective on data languages recognizable by orbit-finite nominal monoids. For this purpose, we introduce pro-orbit-finite nominal topological spaces. Assuming globally bounded support sizes, they coincide with nominal Stone spaces and are shown to be dually equivalent to a subcategory of nominal boolean algebras. Recognizable data languages are characterized as topologically clopen sets of pro-orbit-finite words. In addition, we explore the expressive power of pro-orbit-finite equations by establishing a nominal version of Reiterman’s pseudovariety theorem.
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Fabian Birkmann, Stefan Milius, and Henning Urbat. Nominal Topology for Data Languages. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 114:1-114:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{birkmann_et_al:LIPIcs.ICALP.2023.114,
  author =	{Birkmann, Fabian and Milius, Stefan and Urbat, Henning},
  title =	{{Nominal Topology for Data Languages}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{114:1--114:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.114},
  URN =		{urn:nbn:de:0030-drops-181662},
  doi =		{10.4230/LIPIcs.ICALP.2023.114},
  annote =	{Keywords: Nominal sets, Stone duality, Profinite space, Data languages}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.38
Supported Sets - A New Foundation for Nominal Sets and Automata

Authors: Thorsten Wißmann

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata and coalgebras in general. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process from finite coalgebras in supported sets to orbit-finite coalgebras in nominal sets. One instance of this process transforms the finite representation of a register automaton in supported sets into its configuration automaton in nominal sets.
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Thorsten Wißmann. Supported Sets - A New Foundation for Nominal Sets and Automata. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wimann:LIPIcs.CSL.2023.38,
  author =	{Wi{\ss}mann, Thorsten},
  title =	{{Supported Sets - A New Foundation for Nominal Sets and Automata}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{38:1--38:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.38},
  URN =		{urn:nbn:de:0030-drops-174992},
  doi =		{10.4230/LIPIcs.CSL.2023.38},
  annote =	{Keywords: Nominal Sets, Monads, LFP-Category, Supported Sets, Coalgebra}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.30
Stateful Structural Operational Semantics

Authors: Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Compositionality of denotational semantics is an important concern in programming semantics. Mathematical operational semantics in the sense of Turi and Plotkin guarantees compositionality, but seen from the point of view of stateful computation it applies only to very fine-grained equivalences that essentially assume unrestricted interference by the environment between any two statements. We introduce the more restrictive stateful SOS rule format for stateful languages. We show that compositionality of two more coarse-grained semantics, respectively given by assuming read-only interference or no interference between steps, remains an undecidable property even for stateful SOS. However, further restricting the rule format in a manner inspired by the cool GSOS formats of Bloom and van Glabbeek, we obtain the streamlined and cool stateful SOS formats, which respectively guarantee compositionality of the two more abstract equivalences.
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Sergey Goncharov, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat. Stateful Structural Operational Semantics. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goncharov_et_al:LIPIcs.FSCD.2022.30,
  author =	{Goncharov, Sergey and Milius, Stefan and Schr\"{o}der, Lutz and Tsampas, Stelios and Urbat, Henning},
  title =	{{Stateful Structural Operational Semantics}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.30},
  URN =		{urn:nbn:de:0030-drops-163111},
  doi =		{10.4230/LIPIcs.FSCD.2022.30},
  annote =	{Keywords: Structural Operational Semantics, Rule Formats, Distributive Laws}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.5
Initial Algebras Without Iteration ((Co)algebraic pearls)

Authors: Jiří Adámek, Stefan Milius, and Lawrence S. Moss

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
The Initial Algebra Theorem by Trnková et al. states, under mild assumptions, that an endofunctor has an initial algebra provided it has a pre-fixed point. The proof crucially depends on transfinitely iterating the functor and in fact shows that, equivalently, the (transfinite) initial-algebra chain stops. We give a constructive proof of the Initial Algebra Theorem that avoids transfinite iteration of the functor. For a given pre-fixed point A of the functor, it uses Pataraia’s theorem to obtain the least fixed point of a monotone function on the partial order formed by all subobjects of A. Thanks to properties of recursive coalgebras, this least fixed point yields an initial algebra. We obtain new results on fixed points and initial algebras in categories enriched over directed-complete partial orders, again without iteration. Using transfinite iteration we equivalently obtain convergence of the initial-algebra chain as an equivalent condition, overall yielding a streamlined version of the original proof.
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Jiří Adámek, Stefan Milius, and Lawrence S. Moss. Initial Algebras Without Iteration ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{adamek_et_al:LIPIcs.CALCO.2021.5,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Milius, Stefan and Moss, Lawrence S.},
  title =	{{Initial Algebras Without Iteration}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.5},
  URN =		{urn:nbn:de:0030-drops-153606},
  doi =		{10.4230/LIPIcs.CALCO.2021.5},
  annote =	{Keywords: Initial algebra, Pataraia’s theorem, recursive coalgebra, initial-algebra chain}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.14
Monads on Categories of Relational Structures

Authors: Chase Ford, Stefan Milius, and Lutz Schröder

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
We introduce a framework for universal algebra in categories of relational structures given by finitary relational signatures and finitary or infinitary Horn theories, with the arity λ of a Horn theory understood as a strict upper bound on the number of premisses in its axioms; key examples include partial orders (λ = ω) or metric spaces (λ = ω₁). We establish a bijective correspondence between λ-accessible enriched monads on the given category of relational structures and a notion of λ-ary algebraic theories (i.e. with operations of arity < λ), with the syntax of algebraic theories induced by the relational signature (e.g. inequations or equations-up-to-ε). We provide a generic sound and complete derivation system for such relational algebraic theories, thus in particular recovering (extensions of) recent systems of this type for monads on partial orders and metric spaces by instantiation. In particular, we present an ω₁-ary algebraic theory of metric completion. The theory-to-monad direction of our correspondence remains true for the case of κ-ary algebraic theories and κ-accessible monads for κ < λ, e.g. for finitary theories over metric spaces.
Cite as

Chase Ford, Stefan Milius, and Lutz Schröder. Monads on Categories of Relational Structures. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ford_et_al:LIPIcs.CALCO.2021.14,
  author =	{Ford, Chase and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{Monads on Categories of Relational Structures}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.14},
  URN =		{urn:nbn:de:0030-drops-153697},
  doi =		{10.4230/LIPIcs.CALCO.2021.14},
  annote =	{Keywords: monads, relational structures, Horn theories, relational logic}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.24
Minimality Notions via Factorization Systems ((Co)algebraic pearls)

Authors: Thorsten Wißmann

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system’s semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality. The abstract notion minimality and minimization live in a general category with a factorization system. We will find criteria on the category that ensure uniqueness, existence, and functoriality of the minimization aspects. The proofs of these results instantiate to those for reachability and observability minimization in the standard coalgebra literature. Finally, we will see how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization.
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Thorsten Wißmann. Minimality Notions via Factorization Systems ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wimann:LIPIcs.CALCO.2021.24,
  author =	{Wi{\ss}mann, Thorsten},
  title =	{{Minimality Notions via Factorization Systems}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{24:1--24:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.24},
  URN =		{urn:nbn:de:0030-drops-153791},
  doi =		{10.4230/LIPIcs.CALCO.2021.24},
  annote =	{Keywords: Coalgebra, Reachability, Observability, Minimization, Factorization System}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.58
A Linear-Time Nominal μ-Calculus with Name Allocation

Authors: Daniel Hausmann, Stefan Milius, and Lutz Schröder

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as {regular nondeterministic nominal automata (RNNAs)} have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-μTL} for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-μTL} allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-μTL} over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter.
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Daniel Hausmann, Stefan Milius, and Lutz Schröder. A Linear-Time Nominal μ-Calculus with Name Allocation. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 58:1-58:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hausmann_et_al:LIPIcs.MFCS.2021.58,
  author =	{Hausmann, Daniel and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{A Linear-Time Nominal \mu-Calculus with Name Allocation}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{58:1--58:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.58},
  URN =		{urn:nbn:de:0030-drops-144987},
  doi =		{10.4230/LIPIcs.MFCS.2021.58},
  annote =	{Keywords: Model checking, linear-time logic, nominal sets}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.4
Nominal Büchi Automata with Name Allocation

Authors: Henning Urbat, Daniel Hausmann, Stefan Milius, and Lutz Schröder

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

Abstract
Infinite words over infinite alphabets serve as models of the temporal development of the allocation and (re-)use of resources over linear time. We approach ω-languages over infinite alphabets in the setting of nominal sets, and study languages of infinite bar strings, i.e. infinite sequences of names that feature binding of fresh names; binding corresponds roughly to reading letters from input words in automata models with registers. We introduce regular nominal nondeterministic Büchi automata (Büchi RNNAs), an automata model for languages of infinite bar strings, repurposing the previously introduced RNNAs over finite bar strings. Our machines feature explicit binding (i.e. resource-allocating) transitions and process their input via a Büchi-type acceptance condition. They emerge from the abstract perspective on name binding given by the theory of nominal sets. As our main result we prove that, in contrast to most other nondeterministic automata models over infinite alphabets, language inclusion of Büchi RNNAs is decidable and in fact elementary. This makes Büchi RNNAs a suitable tool for applications in model checking.
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Henning Urbat, Daniel Hausmann, Stefan Milius, and Lutz Schröder. Nominal Büchi Automata with Name Allocation. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{urbat_et_al:LIPIcs.CONCUR.2021.4,
  author =	{Urbat, Henning and Hausmann, Daniel and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{Nominal B\"{u}chi Automata with Name Allocation}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{4:1--4:16},
  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.2021.4},
  URN =		{urn:nbn:de:0030-drops-143813},
  doi =		{10.4230/LIPIcs.CONCUR.2021.4},
  annote =	{Keywords: Data languages, infinite words, nominal sets, inclusion checking}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.32
Explaining Behavioural Inequivalence Generically in Quasilinear Time

Authors: Thorsten Wißmann, Stefan Milius, and Lutz Schröder

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

Abstract
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class in a given system, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically extracted from the functor; these modalities can be systematically translated into custom sets of modalities in a postprocessing step. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time 𝒪((m+n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was 𝒪(m n).
Cite as

Thorsten Wißmann, Stefan Milius, and Lutz Schröder. Explaining Behavioural Inequivalence Generically in Quasilinear Time. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wimann_et_al:LIPIcs.CONCUR.2021.32,
  author =	{Wi{\ss}mann, Thorsten and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{Explaining Behavioural Inequivalence Generically in Quasilinear Time}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{32:1--32:18},
  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.2021.32},
  URN =		{urn:nbn:de:0030-drops-144094},
  doi =		{10.4230/LIPIcs.CONCUR.2021.32},
  annote =	{Keywords: bisimulation, partition refinement, modal logic, distinguishing formulae, coalgebra}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.28
Coalgebra Encoding for Efficient Minimization

Authors: Hans-Peter Deifel, Stefan Milius, and Thorsten Wißmann

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a fully fledged minimization algorithm and tool by integrating two new aspects: (1) the computation of the transition structure on the minimized state set, and (2) the computation of the reachable part of the given system. In our generic coalgebraic setting these two aspects turn out to be surprisingly non-trivial requiring us to extend the previous theory. In particular, we identify a sufficient condition on encodings of coalgebras, and we show how to augment the existing interface, which encapsulates computations that are specific for the coalgebraic type functor, to make the above extensions possible. Both extensions have linear run time.
Cite as

Hans-Peter Deifel, Stefan Milius, and Thorsten Wißmann. Coalgebra Encoding for Efficient Minimization. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{deifel_et_al:LIPIcs.FSCD.2021.28,
  author =	{Deifel, Hans-Peter and Milius, Stefan and Wi{\ss}mann, Thorsten},
  title =	{{Coalgebra Encoding for Efficient Minimization}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{28:1--28:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.28},
  URN =		{urn:nbn:de:0030-drops-142664},
  doi =		{10.4230/LIPIcs.FSCD.2021.28},
  annote =	{Keywords: Coalgebra, Partition refinement, Transition systems, Minimization}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.24
Towards Constructive Hybrid Semantics

Authors: Tim Lukas Diezel and Sergey Goncharov

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

Abstract
With hybrid systems becoming ever more pervasive, the underlying semantic challenges emerge in their entirety. The need for principled semantic foundations has been recognized previously in the case of discrete computation and discrete data, with subsequent implementations in programming languages and proof assistants. Hybrid systems, contrastingly, do not directly fit into the classical semantic paradigms due to the presence of quite specific "non-programmable" features, such as Zeno behaviour and the inherent indispensable reliance on a notion of continuous time. Here, we analyze the phenomenon of hybrid semantics from a constructive viewpoint. In doing so, we propose a monad-based semantics, generic over a given ordered monoid representing the time domain, hence abstracting from the monoid of constructive reals. We implement our construction as a higher inductive-inductive type in the recent cubical extension of the Agda proof assistant, significantly using state-of-the-art advances of homotopy type theory. We show that classically, i.e. under the axiom of choice, our construction admits a charaterization in terms of directed sequence completion.
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Tim Lukas Diezel and Sergey Goncharov. Towards Constructive Hybrid Semantics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{diezel_et_al:LIPIcs.FSCD.2020.24,
  author =	{Diezel, Tim Lukas and Goncharov, Sergey},
  title =	{{Towards Constructive Hybrid Semantics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{24:1--24:19},
  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.2020.24},
  URN =		{urn:nbn:de:0030-drops-123466},
  doi =		{10.4230/LIPIcs.FSCD.2020.24},
  annote =	{Keywords: Hybrid semantics, Elgot iteration, Homotopy type theory, Agda}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.CALCO.2019.2
From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper)

Authors: Stefan Milius

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
This extended abstract first presents a new category theoretic approach to equationally axiomatizable classes of algebras. This approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered algebras, continuous algebras, quantitative algebras, nominal algebras, or profinite algebras. We present a generic HSP theorem and a sound and complete equational logic, which encompass numerous flavors of equational axiomizations studied in the literature. In addition, we use the generic HSP theorem as a key ingredient to obtain Eilenberg-type correspondences yielding algebraic characterizations of properties of regular machine behaviours. When instantiated for orbit-finite nominal monoids, the generic HSP theorem yields a crucial step for the proof of the first Eilenberg-type variety theorem for data languages.
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Stefan Milius. From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 2:1-2:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{milius:LIPIcs.CALCO.2019.2,
  author =	{Milius, Stefan},
  title =	{{From Equational Specifications of Algebras with Structure to Varieties of Data Languages}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{2:1--2:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.2},
  URN =		{urn:nbn:de:0030-drops-114309},
  doi =		{10.4230/LIPIcs.CALCO.2019.2},
  annote =	{Keywords: Birkhoff theorem, Equational logic, Eilenberg theorem, Data languages}
}
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