6 Search Results for "Hermes, Marc"

Document
DOI: 10.4230/LIPIcs.STACS.2026.41
On the Complexity of Computing Strahler Numbers

Authors: Moses Ganardi and Markus Lohrey

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform NC¹. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number k is shown to be P-complete (resp., PSPACE-complete).
Cite as

Moses Ganardi and Markus Lohrey. On the Complexity of Computing Strahler Numbers. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 41:1-41:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{ganardi_et_al:LIPIcs.STACS.2026.41,
  author =	{Ganardi, Moses and Lohrey, Markus},
  title =	{{On the Complexity of Computing Strahler Numbers}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{41:1--41:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.41},
  URN =		{urn:nbn:de:0030-drops-255301},
  doi =		{10.4230/LIPIcs.STACS.2026.41},
  annote =	{Keywords: Strahler number, circuit complexity classes, context-free grammars}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.8
Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting

Authors: Asta Halkjær From and Anders Schlichtkrull

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

Abstract
Smullyan and Fitting have used abstract consistency properties to great effect in unifying meta-theoretical results in logic. In this paper, we generalize these developments with the help of Isabelle/HOL. We use locales to decompose abstract consistency into general parts, and provide the textbook variants as special cases. Users can assemble their own consistency property for a given logic. The compositionality alleviates the absence of dependent types in Isabelle/HOL. We use our development to mechanize completeness of calculi for three logics: (1) first-order logic where we only instantiate universal quantifiers with already occurring terms, (2) second-order logic over general models, and (3) a recently developed strong hybrid logic with propositional quantification.
Cite as

Asta Halkjær From and Anders Schlichtkrull. Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{from_et_al:LIPIcs.ITP.2025.8,
  author =	{From, Asta Halkj{\ae}r and Schlichtkrull, Anders},
  title =	{{Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness \`{a} la Fitting}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{8:1--8:20},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-246406},
  doi =		{10.4230/LIPIcs.ITP.2025.8},
  annote =	{Keywords: Logic, completeness, abstract consistency property, Isabelle/HOL, locales}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.40
Completeness of First-Order Bi-Intuitionistic Logic

Authors: Dominik Kirst and Ian Shillito

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

Abstract
We provide a succinct and verified completeness proof for first-order bi-intuitionistic logic, relative to constant domain Kripke semantics. By doing so, we make up for the almost-50-year-old substantial mistakes in Rauszer’s foundational work, detected but unresolved by Shillito two years ago. Moreover, an even earlier but historically neglected proof by Klemke has been found to contain at least local errors by Olkhovikov and Badia, that remained unfixed due to the technical complexity of Klemke’s argument. To resolve this unclear situation once and for all, we give a succinct completeness proof, based on and dualising a standard proof for constant domain intuitionistic logic, and verify our constructions using the Coq proof assistant to guarantee correctness.
Cite as

Dominik Kirst and Ian Shillito. Completeness of First-Order Bi-Intuitionistic Logic. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 40:1-40:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kirst_et_al:LIPIcs.CSL.2025.40,
  author =	{Kirst, Dominik and Shillito, Ian},
  title =	{{Completeness of First-Order Bi-Intuitionistic Logic}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{40:1--40:19},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-227979},
  doi =		{10.4230/LIPIcs.CSL.2025.40},
  annote =	{Keywords: bi-intuitionistic logic, first-order logic, completeness, Coq proof assistant}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.19
Modular Verification of Intrusive List and Tree Data Structures in Separation Logic

Authors: Marc Hermes and Robbert Krebbers

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Intrusive linked data structures are commonly used in low-level programming languages such as C for efficiency and to enable a form of generic types. Notably, intrusive versions of linked lists and search trees are used in the Linux kernel and the Boost C++ library. These data structures differ from ordinary data structures in the way that nodes contain only the meta data (i.e. pointers to other nodes), but not the data itself. Instead the programmer needs to embed nodes into the data, thereby avoiding pointer indirections, and allowing data to be part of several data structures. In this paper we address the challenge of specifying and verifying intrusive data structures using separation logic. We aim for modular verification, where we first specify and verify the operations on the nodes (without the data) and then use these specifications to verify clients that attach data. We achieve this by employing a representation predicate that separates the data structure’s node structure from the data that is attached to it. We apply our methodology to singly-linked lists - from which we build cyclic and doubly-linked lists - and binary trees - from which we build binary search trees. All verifications are conducted using the Coq proof assistant, making use of the Iris framework for separation logic.
Cite as

Marc Hermes and Robbert Krebbers. Modular Verification of Intrusive List and Tree Data Structures in Separation Logic. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hermes_et_al:LIPIcs.ITP.2024.19,
  author =	{Hermes, Marc and Krebbers, Robbert},
  title =	{{Modular Verification of Intrusive List and Tree Data Structures in Separation Logic}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.19},
  URN =		{urn:nbn:de:0030-drops-207478},
  doi =		{10.4230/LIPIcs.ITP.2024.19},
  annote =	{Keywords: Separation Logic, Program Verification, Data Structures, Iris, Coq}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.9
An Analysis of Tennenbaum’s Theorem in Constructive Type Theory

Authors: Marc Hermes and Dominik Kirst

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

Abstract
Tennenbaum’s theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit and generalize this result. The chosen framework allows for a synthetic approach to computability theory, by exploiting the fact that, externally, all functions definable in constructive type theory can be shown computable. We internalize this fact by assuming a version of Church’s thesis expressing that any function on natural numbers is representable by a formula in PA. This assumption allows for a conveniently abstract setup to carry out rigorous computability arguments and feasible mechanization. Concretely, we constructivize several classical proofs and present one inherently constructive rendering of Tennenbaum’s theorem, all following arguments from the literature. Concerning the classical proofs in particular, the constructive setting allows us to highlight differences in their assumptions and conclusions which are not visible classically. All versions are accompanied by a unified mechanization in the Coq proof assistant.
Cite as

Marc Hermes and Dominik Kirst. An Analysis of Tennenbaum’s Theorem in Constructive Type Theory. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{hermes_et_al:LIPIcs.FSCD.2022.9,
  author =	{Hermes, Marc and Kirst, Dominik},
  title =	{{An Analysis of Tennenbaum’s Theorem in Constructive Type Theory}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.9},
  URN =		{urn:nbn:de:0030-drops-162909},
  doi =		{10.4230/LIPIcs.FSCD.2022.9},
  annote =	{Keywords: first-order logic, Peano arithmetic, Tennenbaum’s theorem, constructive type theory, Church’s thesis, synthetic computability, Coq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.23
Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq

Authors: Dominik Kirst and Marc Hermes

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We mechanise the undecidability of various first-order axiom systems in Coq, employing the synthetic approach to computability underlying the growing Coq Library of Undecidability Proofs. Concretely, we cover both semantic and deductive entailment in fragments of Peano arithmetic (PA) and Zermelo-Fraenkel set theory (ZF), with their undecidability established by many-one reductions from solvability of Diophantine equations, i.e. Hilbert’s tenth problem (H10), and the Post correspondence problem (PCP), respectively. In the synthetic setting based on the computability of all functions definable in a constructive foundation, such as Coq’s type theory, it suffices to define these reductions as meta-level functions with no need for further encoding in a formalised model of computation. The concrete cases of PA and ZF are prepared by a general synthetic theory of undecidable axiomatisations, focusing on well-known connections to consistency and incompleteness. Specifically, our reductions rely on the existence of standard models, necessitating additional assumptions in the case of full ZF, and all axiomatic extensions still justified by such standard models are shown incomplete. As a by-product of the undecidability of ZF formulated using only membership and no equality symbol, we obtain the undecidability of first-order logic with a single binary relation.
Cite as

Dominik Kirst and Marc Hermes. Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{kirst_et_al:LIPIcs.ITP.2021.23,
  author =	{Kirst, Dominik and Hermes, Marc},
  title =	{{Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.23},
  URN =		{urn:nbn:de:0030-drops-139188},
  doi =		{10.4230/LIPIcs.ITP.2021.23},
  annote =	{Keywords: undecidability, synthetic computability, first-order logic, incompleteness, Peano arithmetic, ZF set theory, constructive type theory, Coq}
}
  • Refine by Type
  • 6 Document/PDF
  • 3 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 2 2025
  • 1 2024
  • 1 2022
  • 1 2021

  • Refine by Author
  • 3 Hermes, Marc
  • 3 Kirst, Dominik
  • 1 From, Asta Halkjær
  • 1 Ganardi, Moses
  • 1 Krebbers, Robbert
  • Show More...

  • Refine by Series/Journal
  • 6 LIPIcs

  • Refine by Classification
  • 2 Theory of computation → Constructive mathematics
  • 2 Theory of computation → Logic and verification
  • 2 Theory of computation → Proof theory
  • 1 Theory of computation → Circuit complexity
  • 1 Theory of computation → Data structures design and analysis
  • Show More...

  • Refine by Keyword
  • 3 Coq
  • 3 first-order logic
  • 2 Peano arithmetic
  • 2 completeness
  • 2 constructive type theory
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact