14 Search Results for "Kappé, Tobias"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.25
A Unifying Categorical View of Nondeterministic Iteration and Tests

Authors: Sergey Goncharov and Tarmo Uustalu

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

Abstract
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of it came along afterwards to answer the demand for more refined flavors of semantics, such as stateful, concurrent, exceptional, hybrid, branching time, etc. We detach Kleene iteration from Kleene algebra and analyze it from the categorical perspective. The notion, we arrive at is that of Kleene-iteration category (with coproducts and tests), which we show to be general and robust in the sense of compatibility with programming language features, such as exceptions, store, concurrent behaviour, etc. We attest the proposed notion w.r.t. various yardsticks, most importantly, by characterizing the free model as a certain category of (nondeterministic) rational trees.
Cite as

Sergey Goncharov and Tarmo Uustalu. A Unifying Categorical View of Nondeterministic Iteration and Tests. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goncharov_et_al:LIPIcs.CONCUR.2024.25,
  author =	{Goncharov, Sergey and Uustalu, Tarmo},
  title =	{{A Unifying Categorical View of Nondeterministic Iteration and Tests}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{25:1--25:22},
  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.2024.25},
  URN =		{urn:nbn:de:0030-drops-207979},
  doi =		{10.4230/LIPIcs.CONCUR.2024.25},
  annote =	{Keywords: Kleene iteration, Elgot iteration, Kleene algebra, coalgebraic resumptions}
}
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)

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@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)

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@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
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)

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@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.
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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)

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@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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.136
Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity

Authors: Wojciech Różowski, Tobias Kappé, Dexter Kozen, Todd Schmid, and Alexandra Silva

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

Abstract
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special class of probabilistic automata. We give a sound and complete Salomaa-style axiomatisation of bisimilarity of ProbGKAT expressions. Finally, we show that bisimilarity of ProbGKAT expressions can be decided in O(n³ log n) time via a generic partition refinement algorithm.
Cite as

Wojciech Różowski, Tobias Kappé, Dexter Kozen, Todd Schmid, and Alexandra Silva. Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 136:1-136:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rozowski_et_al:LIPIcs.ICALP.2023.136,
  author =	{R\'{o}\.{z}owski, Wojciech and Kapp\'{e}, Tobias and Kozen, Dexter and Schmid, Todd and Silva, Alexandra},
  title =	{{Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{136:1--136:20},
  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.2023.136},
  URN =		{urn:nbn:de:0030-drops-181880},
  doi =		{10.4230/LIPIcs.ICALP.2023.136},
  annote =	{Keywords: Kleene Algebra with Tests, program equivalence, completeness, coalgebra}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.142
Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness

Authors: Todd Schmid, Tobias Kappé, Dexter Kozen, and Alexandra Silva

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to these behaviors. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms.
Cite as

Todd Schmid, Tobias Kappé, Dexter Kozen, and Alexandra Silva. Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 142:1-142:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{schmid_et_al:LIPIcs.ICALP.2021.142,
  author =	{Schmid, Todd and Kapp\'{e}, Tobias and Kozen, Dexter and Silva, Alexandra},
  title =	{{Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{142:1--142:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.142},
  URN =		{urn:nbn:de:0030-drops-142118},
  doi =		{10.4230/LIPIcs.ICALP.2021.142},
  annote =	{Keywords: Kleene algebra, program equivalence, completeness, coequations}
}
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)

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@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
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2019.6
An Algebraic Framework to Reason About Concurrency (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Hoare, Struth, and collaborators proposed a concurrent extension of Kleene Algebra (CKA) as a first step towards developing algebraic reasoning for concurrent programs. Completing their research program and extending KAT to encompass concurrent behaviour has however proven to be more challenging than initially expected. The core problem appears because when generalising KAT to reason about concurrent programs, axioms native to KAT in conjunction with expected axioms for reasoning about concurrency lead to an unexpected equation about programs. In this talk, we will revise the literature on CKA(T) and explain the challenges and solutions in the development of an algebraic framework for concurrency. The talk is based on a series of papers joint with Tobias Kappé, Paul Brunet, Bas Luttik, Jurriaan Rot, Jana Wagemaker, and Fabio Zanasi [Tobias Kappé et al., 2017; Tobias Kappé et al., 2019; Kappé et al., 2018]. Additional references can be found on the CoNeCo project website: https://coneco-project.org/.
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Alexandra Silva. An Algebraic Framework to Reason About Concurrency (Invited Talk). In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, p. 6:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{silva:LIPIcs.FSTTCS.2019.6,
  author =	{Silva, Alexandra},
  title =	{{An Algebraic Framework to Reason About Concurrency}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{6:1--6:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.6},
  URN =		{urn:nbn:de:0030-drops-115687},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.6},
  annote =	{Keywords: Kleene Algebra, Concurrency, Automata}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2019.6
Tree Automata as Algebras: Minimisation and Determinisation

Authors: Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, and Alexandra Silva

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

Abstract
We study a categorical generalisation of tree automata, as algebras for a fixed endofunctor endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We then build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting and relate it to the existence of minimal automata. Finally, we show that generalised types of side-effects, such as non-determinism, can be captured by this categorical framework, leading to a general determinisation procedure.
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Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, and Alexandra Silva. Tree Automata as Algebras: Minimisation and Determinisation. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{vanheerdt_et_al:LIPIcs.CALCO.2019.6,
  author =	{van Heerdt, Gerco and Kapp\'{e}, Tobias and Rot, Jurriaan and Sammartino, Matteo and Silva, Alexandra},
  title =	{{Tree Automata as Algebras: Minimisation and Determinisation}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{6:1--6:22},
  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.2019.6},
  URN =		{urn:nbn:de:0030-drops-114341},
  doi =		{10.4230/LIPIcs.CALCO.2019.6},
  annote =	{Keywords: tree automata, algebras, minimisation, determinisation, Nerode equivalence}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2019.2
Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra. We will also discuss how this result has practical implications in the verification of programs, with examples from network and probabilistic programming. This is joint work with Nate Foster, Justin Hsu, Tobias Kappe, Dexter Kozen, and Steffen Smolka.
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Alexandra Silva. Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{silva:LIPIcs.MFCS.2019.2,
  author =	{Silva, Alexandra},
  title =	{{Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.2},
  URN =		{urn:nbn:de:0030-drops-109462},
  doi =		{10.4230/LIPIcs.MFCS.2019.2},
  annote =	{Keywords: Kleene algebra, verification, decision procedures}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.41
Kleene Algebra with Observations

Authors: Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory.
Cite as

Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi. Kleene Algebra with Observations. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kappe_et_al:LIPIcs.CONCUR.2019.41,
  author =	{Kapp\'{e}, Tobias and Brunet, Paul and Rot, Jurriaan and Silva, Alexandra and Wagemaker, Jana and Zanasi, Fabio},
  title =	{{Kleene Algebra with Observations}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.41},
  URN =		{urn:nbn:de:0030-drops-109431},
  doi =		{10.4230/LIPIcs.CONCUR.2019.41},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, free model, axiomatisation, decision procedure}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2017.25
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages

Authors: Tobias Kappé, Paul Brunet, Bas Luttik, Alexandra Silva, and Fabio Zanasi

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this paper makes an important step towards an answer. We present a new automaton model and a Kleene-like theorem that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours.
Cite as

Tobias Kappé, Paul Brunet, Bas Luttik, Alexandra Silva, and Fabio Zanasi. Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kappe_et_al:LIPIcs.CONCUR.2017.25,
  author =	{Kapp\'{e}, Tobias and Brunet, Paul and Luttik, Bas and Silva, Alexandra and Zanasi, Fabio},
  title =	{{Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.25},
  URN =		{urn:nbn:de:0030-drops-77913},
  doi =		{10.4230/LIPIcs.CONCUR.2017.25},
  annote =	{Keywords: Kleene theorem, Series-rational expressions, Automata, Brzozowski derivatives, Concurrency, Pomsets}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.3
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this talk will overview why the problem is so difficult. We will then pave the way towards a solution, by presenting a new automaton model and a Kleene-like theorem for CKA. More precisely, we connect a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours. We also survey how the present work can be used to to extend the network specification language NetKAT with primitives for concurrency so as to model and reason about concurrency within networks. This is joint work with Tobias Kappe, Paul Brunet, Bas Luttik, and Fabio Zanasi.
Cite as

Alexandra Silva. Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{silva:LIPIcs.FSCD.2017.3,
  author =	{Silva, Alexandra},
  title =	{{Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.3},
  URN =		{urn:nbn:de:0030-drops-77445},
  doi =		{10.4230/LIPIcs.FSCD.2017.3},
  annote =	{Keywords: Kleene algebras, Pomset languages, concurrency, NetKAT}
}
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