Document

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

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To tackle this issue, a number of sub-classes of non-deterministic automata have been identified, all admitting canonical minimal representatives. In previous work, we have shown that such representatives can be recovered categorically in two steps. First, one constructs the minimal bialgebra accepting a given regular language, by closing the minimal coalgebra with additional algebraic structure over a monad. Second, one identifies canonical generators for the algebraic part of the bialgebra, to derive an equivalent coalgebra with side effects in a monad. In this paper, we further develop the general theory underlying these two steps. On the one hand, we show that deriving a minimal bialgebra from a minimal coalgebra can be realized by applying a monad on an appropriate category of subobjects. On the other hand, we explore the abstract theory of generators and bases for algebras over a monad.

Stefan Zetzsche, Alexandra Silva, and Matteo Sammartino. Generators and Bases for Monadic Closures. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 11:1-11:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{zetzsche_et_al:LIPIcs.CALCO.2023.11, author = {Zetzsche, Stefan and Silva, Alexandra and Sammartino, Matteo}, title = {{Generators and Bases for Monadic Closures}}, booktitle = {10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)}, pages = {11:1--11:19}, 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.2023.11}, URN = {urn:nbn:de:0030-drops-188084}, doi = {10.4230/LIPIcs.CALCO.2023.11}, annote = {Keywords: Monads, Category Theory, Generators, Automata, Coalgebras, Bialgebras} }

Document

**Published in:** LIPIcs, Volume 263, 37th European Conference on Object-Oriented Programming (ECOOP 2023)

The preceding decade has seen significant interest in use of active learning to build models of programs and protocols. But existing algorithms assume the existence of an idealized oracle - a so-called Minimally Adequate Teacher (MAT) - that cannot be fully realized in practice and so is usually approximated with testing. This work proposes a new framework for active learning based on an incomplete teacher. This new formulation, called iMAT, neatly handles scenarios in which the teacher has access to only a finite number of tests or otherwise has gaps in its knowledge. We adapt Angluin’s L^⋆ algorithm for learning finite automata to incomplete teachers and we build a prototype implementation in OCaml that uses an SMT solver to help fill in information not supplied by the teacher. We demonstrate the behavior of our iMAT prototype on a variety of learning problems from a standard benchmark suite.

Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva. Automata Learning with an Incomplete Teacher. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 21:1-21:30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{moeller_et_al:LIPIcs.ECOOP.2023.21, author = {Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra}, title = {{Automata Learning with an Incomplete Teacher}}, booktitle = {37th European Conference on Object-Oriented Programming (ECOOP 2023)}, pages = {21:1--21:30}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-281-5}, ISSN = {1868-8969}, year = {2023}, volume = {263}, editor = {Ali, Karim and Salvaneschi, Guido}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2023.21}, URN = {urn:nbn:de:0030-drops-182145}, doi = {10.4230/LIPIcs.ECOOP.2023.21}, annote = {Keywords: Finite Automata, Active Learning, SMT Solvers} }

Document

Artifact

**Published in:** DARTS, Volume 9, Issue 2, Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023)

We provide an implementation of the automata learning software described in the associated ECOOP article. In particular, the artifact is a Docker image with the source code for nerode and nerode-learn, along with the scripts and benchmark inputs needed to reproduce the experiments described in the paper.

Mark Moeller, Thomas Wiener, Alaia Solko-Breslin, Caleb Koch, Nate Foster, and Alexandra Silva. Automata Learning with an Incomplete Teacher (Artifact). In Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 2, pp. 21:1-21:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@Article{moeller_et_al:DARTS.9.2.21, author = {Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra}, title = {{Automata Learning with an Incomplete Teacher (Artifact)}}, pages = {21:1--21:3}, journal = {Dagstuhl Artifacts Series}, ISSN = {2509-8195}, year = {2023}, volume = {9}, number = {2}, editor = {Moeller, Mark and Wiener, Thomas and Solko-Breslin, Alaia and Koch, Caleb and Foster, Nate and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DARTS.9.2.21}, URN = {urn:nbn:de:0030-drops-182612}, doi = {10.4230/DARTS.9.2.21}, annote = {Keywords: Finite Automata, Active Learning, SMT Solvers} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

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

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.

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

Complete Volume

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

LIPIcs, Volume 241, MFCS 2022, Complete Volume

Stefan Szeider, Robert Ganian, and Alexandra Silva. LIPIcs, Volume 241, MFCS 2022, Complete Volume. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 1-1236, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@Proceedings{szeider_et_al:LIPIcs.MFCS.2022, title = {{LIPIcs, Volume 241, MFCS 2022, Complete Volume}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {1--1236}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert 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.MFCS.2022}, URN = {urn:nbn:de:0030-drops-167975}, doi = {10.4230/LIPIcs.MFCS.2022}, annote = {Keywords: LIPIcs, Volume 241, MFCS 2022, Complete Volume} }

Document

Front Matter

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Front Matter, Table of Contents, Preface, Conference Organization

Stefan Szeider, Robert Ganian, and Alexandra Silva. Front Matter, Table of Contents, Preface, Conference Organization. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 0:i-0:xviii, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{szeider_et_al:LIPIcs.MFCS.2022.0, author = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {0:i--0:xviii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert 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.MFCS.2022.0}, URN = {urn:nbn:de:0030-drops-167981}, doi = {10.4230/LIPIcs.MFCS.2022.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

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

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.

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)

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@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

Complete Volume

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

LIPIcs, Volume 211, CALCO 2021, Complete Volume

Fabio Gadducci and Alexandra Silva. LIPIcs, Volume 211, CALCO 2021, Complete Volume. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 1-384, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@Proceedings{gadducci_et_al:LIPIcs.CALCO.2021, title = {{LIPIcs, Volume 211, CALCO 2021, Complete Volume}}, booktitle = {9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)}, pages = {1--384}, 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}, URN = {urn:nbn:de:0030-drops-153544}, doi = {10.4230/LIPIcs.CALCO.2021}, annote = {Keywords: LIPIcs, Volume 211, CALCO 2021, Complete Volume} }

Document

Front Matter

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

Front Matter, Table of Contents, Preface, Conference Organization

Fabio Gadducci and Alexandra Silva. Front Matter, Table of Contents, Preface, Conference Organization. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 0:i-0:x, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gadducci_et_al:LIPIcs.CALCO.2021.0, author = {Gadducci, Fabio and Silva, Alexandra}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)}, pages = {0:i--0:x}, 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.2021.0}, URN = {urn:nbn:de:0030-drops-153559}, doi = {10.4230/LIPIcs.CALCO.2021.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

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

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.

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

Invited Paper

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

This short article announces the recipients of the CONCUR Test-of-Time Award 2020.

Luca Aceto, Jos Baeten, Patricia Bouyer-Decitre, Holger Hermanns, and Alexandra Silva. CONCUR Test-Of-Time Award 2020 Announcement (Invited Paper). In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 5:1-5:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aceto_et_al:LIPIcs.CONCUR.2020.5, author = {Aceto, Luca and Baeten, Jos and Bouyer-Decitre, Patricia and Hermanns, Holger and Silva, Alexandra}, title = {{CONCUR Test-Of-Time Award 2020 Announcement}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {5:1--5:3}, 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.2020.5}, URN = {urn:nbn:de:0030-drops-128172}, doi = {10.4230/LIPIcs.CONCUR.2020.5}, annote = {Keywords: Concurrency, CONCUR Test-of-Time Award} }

Document

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

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.

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

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

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.

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)

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@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} }

Document

Invited Talk

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

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/.

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

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

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.

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} }

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Invited Talk

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

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.

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} }

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

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.

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} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Nominal automata are a widely studied class of automata designed to recognise languages over infinite alphabets. In this paper, we present a Kleene theorem for nominal automata by providing a syntax to denote regular nominal languages. We use regular expressions with explicit binders for creation and destruction of names and pinpoint an exact property of these expressions - namely memory-finiteness - identifying a subclass of expressions denoting exactly regular nominal languages.

Paul Brunet and Alexandra Silva. A Kleene Theorem for Nominal Automata (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 107:1-107:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brunet_et_al:LIPIcs.ICALP.2019.107, author = {Brunet, Paul and Silva, Alexandra}, title = {{A Kleene Theorem for Nominal Automata}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {107:1--107:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.107}, URN = {urn:nbn:de:0030-drops-106834}, doi = {10.4230/LIPIcs.ICALP.2019.107}, annote = {Keywords: Kleene Theorem, Nominal automata, Bracket Algebra} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

We introduce Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1. Formally, we define ASP using a final coalgebra semantics of programs inspired by Kerstan and König. Then, we introduce a core language for probabilistic streams and trees, and provide two approaches to verify ASP: a syntactic sufficient criterion, and a decision procedure by reduction to model{-}checking LTL formulas on probabilistic pushdown automata.

Alejandro Aguirre, Gilles Barthe, Justin Hsu, and Alexandra Silva. Almost Sure Productivity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 113:1-113:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{aguirre_et_al:LIPIcs.ICALP.2018.113, author = {Aguirre, Alejandro and Barthe, Gilles and Hsu, Justin and Silva, Alexandra}, title = {{Almost Sure Productivity}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {113:1--113:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.113}, URN = {urn:nbn:de:0030-drops-91174}, doi = {10.4230/LIPIcs.ICALP.2018.113}, annote = {Keywords: Coinduction, Probabilistic Programming, Productivity} }

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

Probabilistic automata (PA) combine probability and nondeterminism.
They can be given different semantics, like strong bisimilarity,
convex bisimilarity, or (more recently) distribution bisimilarity.
The latter is based on the view of PA as transformers of probability
distributions, also called belief states, and promotes distributions
to first-class citizens.
We give a coalgebraic account of the latter semantics, and explain
the genesis of the belief-state transformer from a PA. To do so, we
make explicit the convex algebraic structure present in PA and
identify belief-state transformers as transition systems with state
space that carries a convex algebra. As a consequence of our abstract
approach, we can give a sound proof technique which we call
bisimulation up-to convex hull.

Filippo Bonchi, Alexandra Silva, and Ana Sokolova. The Power of Convex Algebras. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 23:1-23:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bonchi_et_al:LIPIcs.CONCUR.2017.23, author = {Bonchi, Filippo and Silva, Alexandra and Sokolova, Ana}, title = {{The Power of Convex Algebras}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {23:1--23:18}, 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.2017.23}, URN = {urn:nbn:de:0030-drops-77966}, doi = {10.4230/LIPIcs.CONCUR.2017.23}, annote = {Keywords: belief-state transformers, bisimulation up-to, coalgebra, convex algebra, convex powerset monad, probabilistic automata} }

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

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.

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} }

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Invited Talk

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

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.

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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**Published in:** LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata have to be developed from scratch because there was no abstract theory offering guidelines. This makes it hard to devise such algorithms, and it obscures their correctness proofs. We introduce a simple category-theoretic formalism that provides an appropriately abstract foundation for studying automata learning. Furthermore, our framework establishes formal relations between algorithms for learning, testing, and minimization. We illustrate its generality with two examples: deterministic and weighted automata.

Gerco van Heerdt, Matteo Sammartino, and Alexandra Silva. CALF: Categorical Automata Learning Framework. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 29:1-29:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{vanheerdt_et_al:LIPIcs.CSL.2017.29, author = {van Heerdt, Gerco and Sammartino, Matteo and Silva, Alexandra}, title = {{CALF: Categorical Automata Learning Framework}}, booktitle = {26th EACSL Annual Conference on Computer Science Logic (CSL 2017)}, pages = {29:1--29:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-045-3}, ISSN = {1868-8969}, year = {2017}, volume = {82}, editor = {Goranko, Valentin and Dam, Mads}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.29}, URN = {urn:nbn:de:0030-drops-76950}, doi = {10.4230/LIPIcs.CSL.2017.29}, annote = {Keywords: automata learning, category theory} }

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Invited Talk

**Published in:** LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

The area of automata learning was pioneered by Angluin in the 80's. Her original algorithm, which applied to regular languages and deterministic automata, has been extended to various types of automata and used in software and hardware verification. In this talk, we will take an abstract perspective at automata learning. We show how the correctness of the original algorithm and many extensions can be captured in one proof using coalgebraic techniques. We also show that a novel algorithm for nominal automata can be derived from the abstract framework.

Alexandra Silva. Coalgebraic Learning (Invited Talk). In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, p. 5:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{silva:LIPIcs.CSL.2016.5, author = {Silva, Alexandra}, title = {{Coalgebraic Learning}}, booktitle = {25th EACSL Annual Conference on Computer Science Logic (CSL 2016)}, pages = {5:1--5:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-022-4}, ISSN = {1868-8969}, year = {2016}, volume = {62}, editor = {Talbot, Jean-Marc and Regnier, Laurent}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.5}, URN = {urn:nbn:de:0030-drops-65455}, doi = {10.4230/LIPIcs.CSL.2016.5}, annote = {Keywords: Automata learning, coalgebraic techniques} }

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Invited Paper

**Published in:** LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Networks have received widespread attention in recent years as a target for domain-specific language design. The emergence of software-defined networking (SDN) as a popular paradigm for network programming has led to the appearance of a number of SDN programming languages seeking to provide high-level abstractions to simplify the task of specifying the packet-processing behavior of a network.
Previous work by Anderson et al. [Anderson et al.,POPL'14,2014] introduced NetKAT, a language and logic for specifying and verifying the packet-processing behavior of networks. NetKAT provides general-purpose programming constructs such as parallel and sequential composition, conditional tests, and iteration, as well as special-purpose primitives for querying and modifying packet headers and encoding network topologies. In contrast to competing approaches, NetKAT has a formal mathematical semantics and an equational deductive system that is sound and complete over that semantics, as well as a PSPACE decision procedure. It is based on Kleene algebra with tests (KAT), an algebraic system for propositional program verification that has been extensively studied for nearly two decades [Kozen,ACM Trans. Program. Lang. Syst.,1997]. Several practical applications of NetKAT have been developed, including algorithms for testing reachability and non-interference and a syntactic correctness proof for a compiler that translates programs to hardware instructions for SDN switches.
In a follow-up paper [Foster et al.,POPL'15,2015], the coalgebraic theory of NetKAT was developed and a bisimulation-based algorithm for deciding equivalence was devised. The new algorithm was shown to be significantly more efficient than the previous naive algorithm [Anderson et al.,POPL'14,2014], which was PSPACE in the best case and the worst case, as it was based on the determinization of a nondeterministic algorithm. Along with the coalgebraic model of NetKAT, the authors presented a specialized version of the Brzozowski derivative in both semantic and syntactic forms. They also also proved a version of Kleene's theorem for NetKAT that shows that the coalgebraic model is equivalent to the standard packet-processing and language models introduced previously [Anderson et al.,POPL'14,2014]. They demonstrated the real-world applicability of the tool by using it to decide common network verification questions such as all-pairs connectivity, loop-freedom, and translation validation - all pressing questions in modern networks.
This talk will survey applications of automata theory, concurrency theory and coalgebra to problems in networking. We will suggest directions for exploring the bridge between the two communities and ways to deliver new synergies. On the one hand, this will lead to new insights and techniques that will enable the development of rigorous semantic foundations for networks. On the other hand, the idysiocransies of networks will provide new challenges for the automata and concurrency community.

Alexandra Silva. Applications of Automata and Concurrency Theory in Networks (Invited Paper). In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 42-43, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{silva:LIPIcs.CONCUR.2015.42, author = {Silva, Alexandra}, title = {{Applications of Automata and Concurrency Theory in Networks}}, booktitle = {26th International Conference on Concurrency Theory (CONCUR 2015)}, pages = {42--43}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-91-0}, ISSN = {1868-8969}, year = {2015}, volume = {42}, editor = {Aceto, Luca and de Frutos Escrig, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.42}, URN = {urn:nbn:de:0030-drops-53993}, doi = {10.4230/LIPIcs.CONCUR.2015.42}, annote = {Keywords: Automata, network programming, coalgebra} }

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**Published in:** LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers.

Jörg Endrullis, Helle Hvid Hansen, Dimitri Hendriks, Andrew Polonsky, and Alexandra Silva. A Coinductive Framework for Infinitary Rewriting and Equational Reasoning. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 143-159, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{endrullis_et_al:LIPIcs.RTA.2015.143, author = {Endrullis, J\"{o}rg and Hansen, Helle Hvid and Hendriks, Dimitri and Polonsky, Andrew and Silva, Alexandra}, title = {{A Coinductive Framework for Infinitary Rewriting and Equational Reasoning}}, booktitle = {26th International Conference on Rewriting Techniques and Applications (RTA 2015)}, pages = {143--159}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-85-9}, ISSN = {1868-8969}, year = {2015}, volume = {36}, editor = {Fern\'{a}ndez, Maribel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.143}, URN = {urn:nbn:de:0030-drops-51949}, doi = {10.4230/LIPIcs.RTA.2015.143}, annote = {Keywords: infinitary rewriting, coinduction} }

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**Published in:** LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor $F$ determines both the type of systems ($F$-coalgebras) and a notion of behavioral
equivalence ($\sim_F$) amongst them. Many types of transition systems and their equivalences can be captured by a functor $F$. For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity. The powerset construction is a standard method for converting a nondeterministic automaton into an equivalent deterministic one as far as language is concerned. In this paper, we lift the powerset construction on automata to the more general framework of coalgebras with structured state spaces. Examples of applications include partial Mealy machines, (structured) Moore automata, and Rabin probabilistic automata.

Alexandra Silva, Filippo Bonchi, Marcello M. Bonsangue, and Jan J. M. M. Rutten. Generalizing the powerset construction, coalgebraically. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 272-283, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

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@InProceedings{silva_et_al:LIPIcs.FSTTCS.2010.272, author = {Silva, Alexandra and Bonchi, Filippo and Bonsangue, Marcello M. and Rutten, Jan J. M. M.}, title = {{Generalizing the powerset construction, coalgebraically}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {272--283}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-23-1}, ISSN = {1868-8969}, year = {2010}, volume = {8}, editor = {Lodaya, Kamal and Mahajan, Meena}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.272}, URN = {urn:nbn:de:0030-drops-28706}, doi = {10.4230/LIPIcs.FSTTCS.2010.272}, annote = {Keywords: coalgebra, language equivalence, bisimilarity, powerset construction} }

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