26 Search Results for "Pous, Damien"

Document
DOI: 10.4230/LIPIcs.ITP.2025.36
Verifying Datalog Reasoning with Lean

Authors: Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Datalog is an essential logical rule language with many applications, and modern rule engines compute logical consequences for Datalog with high performance and scalability. While Datalog is rather simple and, in principle, explainable by design, such sophisticated implementations and optimizations are hard to verify. We therefore propose a certificate-based approach to validate results of Datalog reasoners in a formally verified checker for Datalog proofs. Using the proof assistant Lean, we implement such a checker and verify its correctness against direct formalizations of the Datalog semantics. We propose two JSON encodings for Datalog proofs: one using the widely supported Datalog proof trees, and one using directed acyclic graphs for succinctness. To evaluate the practical feasibility and performance of our approach, we validate proofs that we obtain by converting derivation traces of an existing Datalog reasoner into our tool-independent format.
Cite as

Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch. Verifying Datalog Reasoning with Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tantow_et_al:LIPIcs.ITP.2025.36,
  author =	{Tantow, Johannes and Gerlach, Lukas and Mennicke, Stephan and Kr\"{o}tzsch, Markus},
  title =	{{Verifying Datalog Reasoning with Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.36},
  URN =		{urn:nbn:de:0030-drops-246342},
  doi =		{10.4230/LIPIcs.ITP.2025.36},
  annote =	{Keywords: Certifying Algorithms, Datalog, Formal Verification}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2025.39
Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search (Short Paper)

Authors: Nadeem Abdul Hamid

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The concept of permutations is fundamental in computer science, and is useful for specifying and reasoning about a variety of data structures and algorithms. This paper presents the implementation of a fully automated tactic for proving complex permutation goals within the Rocq Prover (formerly, Coq proof assistant). Our approach leverages proof by reflection and an iterative deepening search procedure to establish permutation relations on arbitrary lists composed of concatenation operations. We detail the construction of mapping/substitution environments, a unification algorithm, and metaprogramming tactics to automate the proof process. The potential impact of the tactic for goals involving permutations is demonstrated by significant reduction in proof script length for an existing non-trivial development.
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Nadeem Abdul Hamid. Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 39:1-39:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abdulhamid:LIPIcs.ITP.2025.39,
  author =	{Abdul Hamid, Nadeem},
  title =	{{Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{39:1--39:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.39},
  URN =		{urn:nbn:de:0030-drops-246378},
  doi =		{10.4230/LIPIcs.ITP.2025.39},
  annote =	{Keywords: permutations, reflection, tactics, Rocq, Coq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.30
Nondeterministic Asynchronous Dataflow in Isabelle/HOL

Authors: Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We formalize nondeterministic asynchronous dataflow networks in Isabelle/HOL. Dataflow networks are comprised of operators that are capable of communicating with the network, performing silent computations, and making nondeterministic choices. We represent operators using a shallow embedding as codatatypes. Using this representation, we define standard asynchronous dataflow primitives, including sequential and parallel composition and a feedback operator. These primitives adhere to a number of laws from the literature, which we prove by coinduction using weak bisimilarity as our equality. Albeit coinductive and nondeterministic, our model is executable via code extraction to Haskell.
Cite as

Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel. Nondeterministic Asynchronous Dataflow in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{silva_et_al:LIPIcs.ITP.2025.30,
  author =	{Silva, Rafael Castro Gon\c{c}alves and Fernet, Laouen and Traytel, Dmitriy},
  title =	{{Nondeterministic Asynchronous Dataflow in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.30},
  URN =		{urn:nbn:de:0030-drops-246280},
  doi =		{10.4230/LIPIcs.ITP.2025.30},
  annote =	{Keywords: dataflow, verification, coinduction, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.10
An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems

Authors: Dohan Kim

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a formalized framework for semi-Thue and conditional semi-Thue systems for studying monoids and their word problem using the Isabelle/HOL proof assistant. We provide a formalized decision procedure for the word problem of monoids if they are finitely presented by complete semi-Thue systems. In particular, we present a new formalized method for checking confluence using (conditional) critical pairs for certain conditional semi-Thue systems. We propose and formalize an inference system for generating conditional equational theories and Thue congruences using conditional semi-Thue systems. Then we provide a new formalized decision procedure for the word problem of monoids which have finite complete (reductive) conditional presentations.
Cite as

Dohan Kim. An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim:LIPIcs.ITP.2025.10,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.10},
  URN =		{urn:nbn:de:0030-drops-246081},
  doi =		{10.4230/LIPIcs.ITP.2025.10},
  annote =	{Keywords: semi-Thue systems, conditional semi-Thue systems, conditional string rewriting, monoids, word problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.39
Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points

Authors: Anupam Das and Abhishek De

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely unexplored. In recent work [Anupam Das and Abhishek De, 2024], a notation for non-deterministic finite automata (NFAs) was introduced, along with a sound and complete axiomatisation of their equational theory via right-linear algebras. In this paper, we extend that line of work to the setting of infinite words. In particular, we present a dualised syntax, yielding a notation for APAs based on right-linear lattice expressions, and provide a natural axiomatisation of their equational theory with respect to the standard language model of ω-regular languages. The design of this axiomatisation is guided by the theory of fixed point logics; in fact, the completeness factors cleanly through the completeness of the linear-time μ-calculus.
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Anupam Das and Abhishek De. Right-Linear Lattices: An Algebraic Theory of ω-Regular Languages, with Fixed Points. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{das_et_al:LIPIcs.MFCS.2025.39,
  author =	{Das, Anupam and De, Abhishek},
  title =	{{Right-Linear Lattices: An Algebraic Theory of \omega-Regular Languages, with Fixed Points}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.39},
  URN =		{urn:nbn:de:0030-drops-241461},
  doi =		{10.4230/LIPIcs.MFCS.2025.39},
  annote =	{Keywords: omega-languages, regular languages, fixed points, Kleene algebras, right-linear grammars}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.21
An Expressive Trace Logic for Recursive Programs

Authors: Dilian Gurov and Reiner Hähnle

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We present an expressive logic over trace formulas, based on binary state predicates, chop, and least fixed points, for precise specification of programs with recursive procedures. Both programs and trace formulas are equipped with a direct-style, fully compositional, denotational semantics that on programs coincides with the standard SOS of recursive programs. We design a compositional proof calculus for proving finite-trace program properties, and prove soundness as well as (relative) completeness. We show that each program can be mapped to a semantics-preserving trace formula and, vice versa, each trace formula can be mapped to a canonical program over slightly extended programs, resulting in a Galois connection between programs and formulas. Our results shed light on the correspondence between programming constructs and logical connectives.
Cite as

Dilian Gurov and Reiner Hähnle. An Expressive Trace Logic for Recursive Programs. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gurov_et_al:LIPIcs.FSCD.2025.21,
  author =	{Gurov, Dilian and H\"{a}hnle, Reiner},
  title =	{{An Expressive Trace Logic for Recursive Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  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.FSCD.2025.21},
  URN =		{urn:nbn:de:0030-drops-236360},
  doi =		{10.4230/LIPIcs.FSCD.2025.21},
  annote =	{Keywords: Denotational semantics, compositional semantics, program specification, compositional verification, fixed point logic, trace logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.28
Strong Induction Is an Up-To Technique

Authors: Filippo Bonchi, Elena Di Lavore, and Anna Ricci

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Up-to techniques are enhancements of the coinduction proof principle which, in lattice theoretic terms, is the dual of induction. What is the dual of coinduction up-to? By means of duality, we illustrate a theory of induction up-to and we observe that an elementary proof technique, commonly known as strong induction, is an instance of induction up-to. We also show that, when generalising our theory from lattices to categories, one obtains an enhancement of the induction definition principle known in the literature as comonadic recursion.
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Filippo Bonchi, Elena Di Lavore, and Anna Ricci. Strong Induction Is an Up-To Technique. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CSL.2025.28,
  author =	{Bonchi, Filippo and Di Lavore, Elena and Ricci, Anna},
  title =	{{Strong Induction Is an Up-To Technique}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.28},
  URN =		{urn:nbn:de:0030-drops-227856},
  doi =		{10.4230/LIPIcs.CSL.2025.28},
  annote =	{Keywords: Induction, Coinduction, Up-to Techniques, Induction up-to, Lattices, Algebras}
}
Artifact
Software
DOI: 10.4230/artifacts.22445
Hypergraphs

Authors: Damien Pous

Abstract
Cite as

Damien Pous. Hypergraphs (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22445,
   title = {{Hypergraphs}}, 
   author = {Pous, Damien},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:028863b2f75dde258591611a6c7c165e289db890;origin=https://github.com/damien-pous/hypergraph;visit=swh:1:snp:76c08bf95d77951c90bdd771a828219ebb4cdcd2;anchor=swh:1:rev:661b5ef93f9d6a2f450f6f0638a1b61780dfe0a4}{\texttt{swh:1:dir:028863b2f75dde258591611a6c7c165e289db890}} (visited on 2024-11-28)},
   url = {https://perso.ens-lyon.fr/damien.pous/hypergraph/},
   doi = {10.4230/artifacts.22445},
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.135
A Finite Presentation of Graphs of Treewidth at Most Three

Authors: Amina Doumane, Samuel Humeau, and Damien Pous

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

Abstract
We provide a finite equational presentation of graphs of treewidth at most three, solving an instance of an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small interface. We introduce appropriate notions of connectivity for such graphs (components, cutvertices, separation pairs). We use those concepts to analyse the structure of graphs of treewidth at most three, showing how they can be decomposed recursively, first canonically into connected parallel components, and then non-deterministically. The main difficulty consists in showing that all non-deterministic choices can be related using only finitely many equational axioms.
Cite as

Amina Doumane, Samuel Humeau, and Damien Pous. A Finite Presentation of Graphs of Treewidth at Most Three. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 135:1-135:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doumane_et_al:LIPIcs.ICALP.2024.135,
  author =	{Doumane, Amina and Humeau, Samuel and Pous, Damien},
  title =	{{A Finite Presentation of Graphs of Treewidth at Most Three}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{135:1--135:18},
  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.2024.135},
  URN =		{urn:nbn:de:0030-drops-202787},
  doi =		{10.4230/LIPIcs.ICALP.2024.135},
  annote =	{Keywords: Graphs, treewidth, connectedness, axiomatisation, series-parallel expressions}
}
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.
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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)

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@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
DOI: 10.4230/LIPIcs.MFCS.2021.41
Graph Characterization of the Universal Theory of Relations

Authors: Amina Doumane

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

Abstract
The equational theory of relations can be characterized using graphs and homomorphisms. This result, found independently by Freyd and Scedrov and by Andréka and Bredikhin, shows that the equational theory of relations is decidable. In this paper, we extend this characterization to the whole universal first-order theory of relations. Using our characterization, we show that the positive universal fragment is also decidable.
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Amina Doumane. Graph Characterization of the Universal Theory of Relations. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{doumane:LIPIcs.MFCS.2021.41,
  author =	{Doumane, Amina},
  title =	{{Graph Characterization of the Universal Theory of Relations}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.41},
  URN =		{urn:nbn:de:0030-drops-144815},
  doi =		{10.4230/LIPIcs.MFCS.2021.41},
  annote =	{Keywords: Relation algebra, Graph homomorphism, Equational theories, First-order logic}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.29
On the Logical Strength of Confluence and Normalisation for Cyclic Proofs

Authors: Anupam Das

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

Abstract
In this work we address the logical strength of confluence and normalisation for non-wellfounded typing derivations, in the tradition of "cyclic proof theory". We present a circular version CT of Gödel's system T, with the aim of comparing the relative expressivity of the theories CT and T. We approach this problem by formalising rewriting-theoretic results such as confluence and normalisation for the underlying "coterm" rewriting system of CT within fragments of second-order arithmetic. We establish confluence of CT within the theory RCA₀, a conservative extension of primitive recursive arithmetic and IΣ1. This allows us to recast type structures of hereditarily recursive operations as "coterm" models of T. We show that these also form models of CT, by formalising a totality argument for circular typing derivations within suitable fragments of second-order arithmetic. Relying on well-known proof mining results, we thus obtain an interpretation of CT into T; in fact, more precisely, we interpret level-n-CT into level-(n+1)-T, an optimum result in terms of abstraction complexity. A direct consequence of these model-theoretic results is weak normalisation for CT. As further results, we also show strong normalisation for CT and continuity of functionals computed by its type 2 coterms.
Cite as

Anupam Das. On the Logical Strength of Confluence and Normalisation for Cyclic Proofs. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{das:LIPIcs.FSCD.2021.29,
  author =	{Das, Anupam},
  title =	{{On the Logical Strength of Confluence and Normalisation for Cyclic Proofs}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.29},
  URN =		{urn:nbn:de:0030-drops-142678},
  doi =		{10.4230/LIPIcs.FSCD.2021.29},
  annote =	{Keywords: confluence, normalisation, system T, circular proofs, reverse mathematics, type structures}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.29
Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms

Authors: Amina Doumane and Damien Pous

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

Abstract
We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of semilattice-ordered semigroups. We show that the equational theory is no longer finitely based when adding one or the other constant, refuting a conjecture from the literature. Our proofs exploit a characterisation in terms of graphs and homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures.
Cite as

Amina Doumane and Damien Pous. Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{doumane_et_al:LIPIcs.CONCUR.2020.29,
  author =	{Doumane, Amina and Pous, Damien},
  title =	{{Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{29:1--29:16},
  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.2020.29},
  URN =		{urn:nbn:de:0030-drops-128411},
  doi =		{10.4230/LIPIcs.CONCUR.2020.29},
  annote =	{Keywords: Relation algebra, graph homomorphisms, (in)equational theories}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.45
Cyclic Proofs and Jumping Automata

Authors: Denis Kuperberg, Laureline Pinault, and Damien Pous

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

Abstract
We consider a fragment of a cyclic sequent proof system for Kleene algebra, and we see it as a computational device for recognising languages of words. The starting proof system is linear and we show that it captures precisely the regular languages. When adding the standard contraction rule, the expressivity raises significantly; we characterise the corresponding class of languages using a new notion of multi-head finite automata, where heads can jump.
Cite as

Denis Kuperberg, Laureline Pinault, and Damien Pous. Cyclic Proofs and Jumping Automata. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kuperberg_et_al:LIPIcs.FSTTCS.2019.45,
  author =	{Kuperberg, Denis and Pinault, Laureline and Pous, Damien},
  title =	{{Cyclic Proofs and Jumping Automata}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{45:1--45:14},
  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.2019.45},
  URN =		{urn:nbn:de:0030-drops-116071},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.45},
  annote =	{Keywords: Cyclic proofs, regular languages, multi-head automata, transducers}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.CALCO.2019.4
Coinduction: Automata, Formal Proof, Companions (Invited Paper)

Authors: Damien Pous

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

Abstract
Coinduction is a mathematical tool that is used pervasively in computer science: to program and reason about infinite data-structures, to give semantics to concurrent systems, to obtain automata algorithms. We present some of these applications in automata theory and in formalised mathematics. Then we discuss recent developments on the abstract theory of coinduction and its enhancements.
Cite as

Damien Pous. Coinduction: Automata, Formal Proof, Companions (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{pous:LIPIcs.CALCO.2019.4,
  author =	{Pous, Damien},
  title =	{{Coinduction: Automata, Formal Proof, Companions}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{4:1--4:4},
  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.2019.4},
  URN =		{urn:nbn:de:0030-drops-114323},
  doi =		{10.4230/LIPIcs.CALCO.2019.4},
  annote =	{Keywords: Coinduction, Automata, Coalgebra, Formal proofs}
}
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