22 Search Results for "Rot, Jurriaan"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.20
Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques

Authors: Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss, Barbara König, Matina Najafi, Wojciech Różowski, and Paul Wild

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Behavioural distances of transition systems modelled via coalgebras for endofunctors generalize traditional notions of behavioural equivalence to a quantitative setting, in which states are equipped with a measure of how (dis)similar they are. Endowing transition systems with such distances essentially relies on the ability to lift functors describing the one-step behavior of the transition systems to the category of pseudometric spaces. We consider the category theoretic generalization of the Kantorovich lifting from transportation theory to the case of lifting functors to quantale-valued relations, which subsumes equivalences, preorders and (directed) metrics. We use tools from fibred category theory, which allow one to see the Kantorovich lifting as arising from an appropriate fibred adjunction. Our main contributions are compositionality results for the Kantorovich lifting, where we show that that the lifting of a composed functor coincides with the composition of the liftings. In addition, we describe how to lift distributive laws in the case where one of the two functors is polynomial (with finite coproducts). These results are essential ingredients for adapting up-to-techniques to the case of quantale-valued behavioural distances. Up-to techniques are a well-known coinductive technique for efficiently showing lower bounds for behavioural distances. We illustrate the results of our paper in two case studies.
Cite as

Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss, Barbara König, Matina Najafi, Wojciech Różowski, and Paul Wild. Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dangelo_et_al:LIPIcs.CONCUR.2024.20,
  author =	{D'Angelo, Keri and Gurke, Sebastian and Kirss, Johanna Maria and K\"{o}nig, Barbara and Najafi, Matina and R\'{o}\.{z}owski, Wojciech and Wild, Paul},
  title =	{{Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.20},
  URN =		{urn:nbn:de:0030-drops-207921},
  doi =		{10.4230/LIPIcs.CONCUR.2024.20},
  annote =	{Keywords: behavioural metrics, coalgebra, Galois connections, quantales, Kantorovich lifting, up-to techniques}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.33
Automating Memory Model Metatheory with Intersections

Authors: Aristotelis Koutsouridis, Michalis Kokologiannakis, and Viktor Vafeiadis

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
In the weak memory consistency literature, the semantics of concurrent programs is typically defined as a constraint on execution graphs, expressed in relational algebra. Prior work has shown that basic metatheoretic questions about memory models are decidable as long as they can be expressed as irreflexivity and emptiness constraints over Kleene Algebra with Tests (KAT), a condition that rules out practical memory models such the C/C++ and the Linux kernel models. In this paper, we extend these results to memory models containing arbitrary intersections with uninterpreted relations. We can thus automatically establish compilation correctness and derive efficient incremental consistency checkers for RC11, LKMM, and other memory models.
Cite as

Aristotelis Koutsouridis, Michalis Kokologiannakis, and Viktor Vafeiadis. Automating Memory Model Metatheory with Intersections. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{koutsouridis_et_al:LIPIcs.CONCUR.2024.33,
  author =	{Koutsouridis, Aristotelis and Kokologiannakis, Michalis and Vafeiadis, Viktor},
  title =	{{Automating Memory Model Metatheory with Intersections}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.33},
  URN =		{urn:nbn:de:0030-drops-208050},
  doi =		{10.4230/LIPIcs.CONCUR.2024.33},
  annote =	{Keywords: Kleene Algebra, Weak Memory Models}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.35
Nominal Tree Automata with Name Allocation

Authors: Simon Prucker and Lutz Schröder

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based on storing data values encountered on the tree in registers for subsequent comparison with further data values. Already on word languages, the expressiveness of such automata models typically increases with the power of control (e.g. deterministic, non-deterministic, alternating). Language inclusion is typically undecidable for non-deterministic or alternating models unless the number of registers is radically restricted, and even then often remains non-elementary. We present an automaton model for data trees that retains a reasonable level of expressiveness, in particular allows non-determinism and any number of registers, while admitting language inclusion checking in elementary complexity, in fact in parametrized exponential time. We phrase the description of our automaton model in the language of nominal sets, building on the recently introduced paradigm of explicit name allocation in nominal automata.
Cite as

Simon Prucker and Lutz Schröder. Nominal Tree Automata with Name Allocation. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{prucker_et_al:LIPIcs.CONCUR.2024.35,
  author =	{Prucker, Simon and Schr\"{o}der, Lutz},
  title =	{{Nominal Tree Automata with Name Allocation}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.35},
  URN =		{urn:nbn:de:0030-drops-208071},
  doi =		{10.4230/LIPIcs.CONCUR.2024.35},
  annote =	{Keywords: Data languages, tree automata, nominal automata, inclusion checking}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.38
Progress, Justness and Fairness in Modal μ-Calculus Formulae

Authors: Myrthe S. C. Spronck, Bas Luttik, and Tim A. C. Willemse

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
When verifying liveness properties on a transition system, it is often necessary to discard spurious violating paths by making assumptions on which paths represent realistic executions. Capturing that some property holds under such an assumption in a logical formula is challenging and error-prone, particularly in the modal μ-calculus. In this paper, we present template formulae in the modal μ-calculus that can be instantiated to a broad range of liveness properties. We consider the following assumptions: progress, justness, weak fairness, strong fairness, and hyperfairness, each with respect to actions. The correctness of these formulae has been proven.
Cite as

Myrthe S. C. Spronck, Bas Luttik, and Tim A. C. Willemse. Progress, Justness and Fairness in Modal μ-Calculus Formulae. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 38:1-38:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{spronck_et_al:LIPIcs.CONCUR.2024.38,
  author =	{Spronck, Myrthe S. C. and Luttik, Bas and Willemse, Tim A. C.},
  title =	{{Progress, Justness and Fairness in Modal \mu-Calculus Formulae}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{38:1--38:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.38},
  URN =		{urn:nbn:de:0030-drops-208102},
  doi =		{10.4230/LIPIcs.CONCUR.2024.38},
  annote =	{Keywords: Modal \mu-calculus, Property specification, Completeness criteria, Progress, Justness, Fairness, Liveness properties}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.149
A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions

Authors: Wojciech Różowski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Deterministic automata have been traditionally studied through the point of view of language equivalence, but another perspective is given by the canonical notion of shortest-distinguishing-word distance quantifying the of states. Intuitively, the longer the word needed to observe a difference between two states, then the closer their behaviour is. In this paper, we give a sound and complete axiomatisation of shortest-distinguishing-word distance between regular languages. Our axiomatisation relies on a recently developed quantitative analogue of equational logic, allowing to manipulate rational-indexed judgements of the form e ≡_ε f meaning term e is approximately equivalent to term f within the error margin of ε. The technical core of the paper is dedicated to the completeness argument that draws techniques from order theory and Banach spaces to simplify the calculation of the behavioural distance to the point it can be then mimicked by axiomatic reasoning.
Cite as

Wojciech Różowski. A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 149:1-149:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rozowski:LIPIcs.ICALP.2024.149,
  author =	{R\'{o}\.{z}owski, Wojciech},
  title =	{{A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{149:1--149:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.149},
  URN =		{urn:nbn:de:0030-drops-202920},
  doi =		{10.4230/LIPIcs.ICALP.2024.149},
  annote =	{Keywords: Regular Expressions, Behavioural Distances, Quantitative Equational Theories}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.157
Domain Reasoning in TopKAT

Authors: Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a relation. This enables several applications in program logics, such as proving under-approximate specifications or reachability properties of imperative programs. However, while TopKAT inherits many pleasant features of KATs, such as having a decidable equational theory, it is incomplete with respect to relational models. In other words, there are properties that hold true of all relational TopKATs but cannot be proved with the axioms of TopKAT. This issue is potentially worrisome for program-logic applications, in which relational models play a key role. In this paper, we further investigate the completeness properties of TopKAT with respect to relational models. We show that TopKAT is complete with respect to (co)domain comparison of KAT terms, but incomplete when comparing the (co)domain of arbitrary TopKAT terms. Since the encoding of under-approximate specifications in TopKAT hinges on this type of formula, the aforementioned incompleteness results have a limited impact when using TopKAT to reason about such specifications.
Cite as

Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi. Domain Reasoning in TopKAT. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 157:1-157:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{zhang_et_al:LIPIcs.ICALP.2024.157,
  author =	{Zhang, Cheng and de Amorim, Arthur Azevedo and Gaboardi, Marco},
  title =	{{Domain Reasoning in TopKAT}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{157:1--157:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.157},
  URN =		{urn:nbn:de:0030-drops-203003},
  doi =		{10.4230/LIPIcs.ICALP.2024.157},
  annote =	{Keywords: Kleene algebra, Kleene Algebra With Tests, Kleene Algebra With Domain, Kleene Algebra With Top and Tests, Completeness, Decidability}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2023.6
Forward and Backward Steps in a Fibration

Authors: Ruben Turkenburg, Harsh Beohar, Clemens Kupke, and Jurriaan Rot

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

Abstract
Distributive laws of various kinds occur widely in the theory of coalgebra, for instance to model automata constructions and trace semantics, and to interpret coalgebraic modal logic. We study steps, which are a general type of distributive law, that allow one to map coalgebras along an adjunction. In this paper, we address the question of what such mappings do to well known notions of equivalence, e.g., bisimilarity, behavioural equivalence, and logical equivalence. We do this using the characterisation of such notions of equivalence as (co)inductive predicates in a fibration. Our main contribution is the identification of conditions on the interaction between the steps and liftings, which guarantees preservation of fixed points by the mapping of coalgebras along the adjunction. We apply these conditions in the context of lax liftings proposed by Bonchi, Silva, Sokolova (2021), and generalise their result on preservation of bisimilarity in the construction of a belief state transformer. Further, we relate our results to properties of coalgebraic modal logics including expressivity and completeness.
Cite as

Ruben Turkenburg, Harsh Beohar, Clemens Kupke, and Jurriaan Rot. Forward and Backward Steps in a Fibration. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{turkenburg_et_al:LIPIcs.CALCO.2023.6,
  author =	{Turkenburg, Ruben and Beohar, Harsh and Kupke, Clemens and Rot, Jurriaan},
  title =	{{Forward and Backward Steps in a Fibration}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{6:1--6:18},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-188032},
  doi =		{10.4230/LIPIcs.CALCO.2023.6},
  annote =	{Keywords: Coalgebra, Fibration, Bisimilarity}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2023.12
Bisimilar States in Uncertain Structures

Authors: Jurriaan Rot and Thorsten Wißmann

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

Abstract
We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms, where one investigates whether two observed behaviours come from the same internal state of a black-box system that can not be transparently inspected. We model this uncertainty as a set functor equipped with a partial order which describes possible future developments of the learning game. On such a functor, we provide a lifting-based definition of uncertain bisimilarity and verify basic properties. Beside its applications to Mealy machines, a natural model for automata learning, our framework also instantiates to an existing compatibility relation on suspension automata, which are used in model-based testing. We show that uncertain bisimilarity is a necessary but not sufficient condition for two states being implementable by the same state in the black-box system. We remedy the lack of sufficiency by a characterization of uncertain bisimilarity in terms of coalgebraic simulations.
Cite as

Jurriaan Rot and Thorsten Wißmann. Bisimilar States in Uncertain Structures. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{rot_et_al:LIPIcs.CALCO.2023.12,
  author =	{Rot, Jurriaan and Wi{\ss}mann, Thorsten},
  title =	{{Bisimilar States in Uncertain Structures}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{12:1--12:17},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-188094},
  doi =		{10.4230/LIPIcs.CALCO.2023.12},
  annote =	{Keywords: Coalgebra, Relation Lifting, Bisimilarity, Mealy Machines, ioco}
}
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.
Cite as

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)

Copy BibTex To Clipboard

@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.CONCUR.2022.26
Completeness Theorems for Kleene Algebra with Top

Authors: Damien Pous and Jana Wagemaker

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We prove two completeness results for Kleene algebra with a top element, with respect to languages and binary relations. While the equational theories of those two classes of models coincide over the signature of Kleene algebra, this is no longer the case when we consider an additional constant "top" for the full element. Indeed, the full relation satisfies more laws than the full language, and we show that those additional laws can all be derived from a single additional axiom. We recover that the two equational theories coincide if we slightly generalise the notion of relational model, allowing sub-algebras of relations where top is a greatest element but not necessarily the full relation. We use models of closed languages and reductions in order to prove our completeness results, which are relative to any axiomatisation of the algebra of regular events.
Cite as

Damien Pous and Jana Wagemaker. Completeness Theorems for Kleene Algebra with Top. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{pous_et_al:LIPIcs.CONCUR.2022.26,
  author =	{Pous, Damien and Wagemaker, Jana},
  title =	{{Completeness Theorems for Kleene Algebra with Top}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir 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.CONCUR.2022.26},
  URN =		{urn:nbn:de:0030-drops-170890},
  doi =		{10.4230/LIPIcs.CONCUR.2022.26},
  annote =	{Keywords: Kleene algebra, Hypotheses, Completeness, Closed languages}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.132
Processes Parametrised by an Algebraic Theory

Authors: Todd Schmid, Wojciech Różowski, Jurriaan Rot, and Alexandra Silva

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic equivalence. We show that there are uniformly defined fragments of our calculi that capture well-known examples from the literature like regular expressions modulo bisimilarity and guarded Kleene algebra with tests. We also derive new calculi for probabilistic and convex processes with an analogue of Kleene star.
Cite as

Todd Schmid, Wojciech Różowski, Jurriaan Rot, and Alexandra Silva. Processes Parametrised by an Algebraic Theory. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 132:1-132:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{schmid_et_al:LIPIcs.ICALP.2022.132,
  author =	{Schmid, Todd and R\'{o}\.{z}owski, Wojciech and Rot, Jurriaan and Silva, Alexandra},
  title =	{{Processes Parametrised by an Algebraic Theory}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{132:1--132:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.132},
  URN =		{urn:nbn:de:0030-drops-164735},
  doi =		{10.4230/LIPIcs.ICALP.2022.132},
  annote =	{Keywords: process algebra, program semantics, coalgebra, regular expressions}
}
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.
Cite as

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)

Copy BibTex To Clipboard

@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
SCICO Journal-first
DOI: 10.4230/LIPIcs.ECOOP.2020.32
A Big Step from Finite to Infinite Computations (SCICO Journal-first)

Authors: Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract
The known is finite, the unknown infinite - Thomas Henry Huxley The behaviour of programs can be described by the final results of computations, and/or their interactions with the context, also seen as observations. For instance, a function call can terminate and return a value, as well as have output effects during its execution. Here, we deal with semantic definitions covering both results and observations. Often, such definitions are provided for finite computations only. Notably, in big-step style, infinite computations are simply not modelled, hence diverging and stuck terms are not distinguished. This becomes even more unsatisfactory if we have observations, since a non-terminating program may have significant infinite behaviour. Recently, examples of big-step semantics modeling divergence have been provided [Davide Ancona et al., 2017; Davide Ancona et al., 2018] by means of generalized inference systems [Davide Ancona et al., 2017; Francesco Dagnino, 2019], which allow corules to control coinduction. Indeed, modeling infinite behaviour by a purely coinductive interpretation of big-step rules would lead to spurious results [Xavier Leroy and Hervé Grall, 2009] and undetermined observation, whereas, by adding appropriate corules, we can correctly get divergence (∞) as the only result, and a uniquely determined observation. This approach has been adopted in [Davide Ancona et al., 2017; Davide Ancona et al., 2018] to design big-step definitions including infinite behaviour for lambda-calculus and a simple imperative Java-like language. However, in such works the designer of the semantics is in charge of finding the appropriate corules, and this is a non-trivial task. In this paper, we show a general construction that extends a given big-step semantics, modeling finite computations, to include infinite behaviour as well, notably by generating appropriate corules. The construction consists of two steps: 1) Starting from a monoid O modeling finite observations (e.g., finite traces), we construct an ω-monoid ⟨O, O_∞⟩ also modeling infinite observations (e.g., infinite traces). The latter structure is a variation of the notion of ω-semigroup [Dominique Perrin and Jean-Eric Pin, 2004], including a mixed product composing a finite with a possibly infinite observation, and an infinite product mapping an infinite sequence of finite observations into a single one (possibly infinite). 2) Starting from an inference system defining a big-step judgment c⇒⟨r, o⟩, with c denoting a configuration, r ∈ R a result, and o ∈ O a finite observation, we construct an inference system with corules defining an extended big-step judgment c⇒c ⇒ ⟨r_∞, o_∞⟩ with r_∞ ∈ R_∞ = R+{∞}, and o_∞ ∈ O_∞ a "possibly infinite" observation. The construction generates additional rules for propagating divergence, and corules for introducing divergence in a controlled way. The exact corules added in the construction depend on the type of observations that one starts with. To show the effectiveness of our approach, we provide several instances of the framework, with different kinds of (finite) observations. Finally, we prove a correctness result for the construction. To this end, we assume the original big-step semantics to be equivalent to (finite sequences of steps in) a reference small-step semantics, and we show that, by applying the construction, we obtain an extended big-step semantics which is still equivalent to the small-step semantics, where we consider possibly infinite sequences of steps.} As hypotheses, rather than {just} equivalence in the finite case {(which would be not enough)}, we assume a set of equivalence conditions between individual big-step rules and the small-step relation. This proof of equivalence holds for deterministic semantics; issues arising in the non-deterministic case and a possible solution are sketched in the conclusion of the full paper.
Cite as

Davide Ancona, Francesco Dagnino, Jurriaan Rot, and Elena Zucca. A Big Step from Finite to Infinite Computations (SCICO Journal-first). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 32:1-32:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{ancona_et_al:LIPIcs.ECOOP.2020.32,
  author =	{Ancona, Davide and Dagnino, Francesco and Rot, Jurriaan and Zucca, Elena},
  title =	{{A Big Step from Finite to Infinite Computations}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{32:1--32:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.32},
  URN =		{urn:nbn:de:0030-drops-131895},
  doi =		{10.4230/LIPIcs.ECOOP.2020.32},
  annote =	{Keywords: Operational semantics, coinduction, infinite behaviour}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.20
Partially Observable Concurrent Kleene Algebra

Authors: Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with variables as well as control structures, such as conditionals and loops, that depend on those variables. We illustrate the use of POCKA through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency.
Cite as

Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva. Partially Observable Concurrent Kleene Algebra. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{wagemaker_et_al:LIPIcs.CONCUR.2020.20,
  author =	{Wagemaker, Jana and Brunet, Paul and Docherty, Simon and Kapp\'{e}, Tobias and Rot, Jurriaan and Silva, Alexandra},
  title =	{{Partially Observable Concurrent Kleene Algebra}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.20},
  URN =		{urn:nbn:de:0030-drops-128324},
  doi =		{10.4230/LIPIcs.CONCUR.2020.20},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, observations, axiomatisation, completeness, sequential consistency}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.77
Preservation of Equations by Monoidal Monads

Authors: Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
If a monad T is monoidal, then operations on a set X can be lifted canonically to operations on TX. In this paper we study structural properties under which T preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as x⋅ y = y) and relevant monads preserve dup equations (where some variable is duplicated, such as x ⋅ x = x). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call n-relevance. Finally, we identify a subclass of equations such that their preservation is equivalent to relevance.
Cite as

Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan. Preservation of Equations by Monoidal Monads. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{parlant_et_al:LIPIcs.MFCS.2020.77,
  author =	{Parlant, Louis and Rot, Jurriaan and Silva, Alexandra and Westerbaan, Bas},
  title =	{{Preservation of Equations by Monoidal Monads}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.77},
  URN =		{urn:nbn:de:0030-drops-127460},
  doi =		{10.4230/LIPIcs.MFCS.2020.77},
  annote =	{Keywords: monoidal monads, algebraic theories, preservation of equations}
}
  • Refine by Author
  • 12 Rot, Jurriaan
  • 6 Silva, Alexandra
  • 3 Kappé, Tobias
  • 3 Pous, Damien
  • 3 Różowski, Wojciech
  • Show More...

  • Refine by Classification
  • 8 Theory of computation → Formal languages and automata theory
  • 3 Theory of computation → Categorical semantics
  • 2 Theory of computation
  • 2 Theory of computation → Concurrency
  • 2 Theory of computation → Logic and verification
  • Show More...

  • Refine by Keyword
  • 6 Coalgebra
  • 2 Automata
  • 2 Bisimilarity
  • 2 Completeness
  • 2 Concurrent Kleene algebra
  • Show More...

  • Refine by Type
  • 22 document

  • Refine by Publication Year
  • 6 2024
  • 5 2020
  • 3 2019
  • 3 2023
  • 2 2022
  • Show More...

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact