4 Search Results for "Fleury, Mathias"

Document
DOI: 10.4230/LIPIcs.SAT.2023.21
Faster LRAT Checking Than Solving with CaDiCaL

Authors: Florian Pollitt, Mathias Fleury, and Armin Biere

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
DRAT is the standard proof format used in the SAT Competition. It is easy to generate but checking proofs often takes even more time than solving the problem. An alternative is to use the LRAT proof system. While LRAT is easier and way more efficient to check, it is more complex to generate directly. Due to this complexity LRAT is not supported natively by any state-of-the-art SAT solver. Therefore Carneiro and Heule proposed the mixed proof format FRAT which still suffers from costly intermediate translation. We present an extension to the state-of-the-art solver CaDiCaL which is able to generate LRAT natively for all procedures implemented in CaDiCaL. We further present Lrat-Trim, a tool which not only trims and checks LRAT proofs in both ASCII and binary format but also produces clausal cores and has been tested thoroughly. Our experiments on recent competition benchmarks show that our approach reduces time of proof generation and certification substantially compared to competing approaches using intermediate DRAT or FRAT proofs.
Cite as

Florian Pollitt, Mathias Fleury, and Armin Biere. Faster LRAT Checking Than Solving with CaDiCaL. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{pollitt_et_al:LIPIcs.SAT.2023.21,
  author =	{Pollitt, Florian and Fleury, Mathias and Biere, Armin},
  title =	{{Faster LRAT Checking Than Solving with CaDiCaL}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.21},
  URN =		{urn:nbn:de:0030-drops-184837},
  doi =		{10.4230/LIPIcs.SAT.2023.21},
  annote =	{Keywords: SAT solving, Proof Checking, DRAT, LRAT, FRAT}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.5
Efficient Full Higher-Order Unification

Authors: Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our unification procedure is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski’s procedure.
Cite as

Petar Vukmirović, Alexander Bentkamp, and Visa Nummelin. Efficient Full Higher-Order Unification. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{vukmirovic_et_al:LIPIcs.FSCD.2020.5,
  author =	{Vukmirovi\'{c}, Petar and Bentkamp, Alexander and Nummelin, Visa},
  title =	{{Efficient Full Higher-Order Unification}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.5},
  URN =		{urn:nbn:de:0030-drops-123271},
  doi =		{10.4230/LIPIcs.FSCD.2020.5},
  annote =	{Keywords: unification, higher-order logic, theorem proving, term rewriting, indexing data structures}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2019.33
The DPRM Theorem in Isabelle (Short Paper)

Authors: Jonas Bayer, Marco David, Abhik Pal, Benedikt Stock, and Dierk Schleicher

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
Hilbert’s 10th problem asks for an algorithm to tell whether or not a given diophantine equation has a solution over the integers. The non-existence of such an algorithm was shown in 1970 by Yuri Matiyasevich. The key step is known as the DPRM theorem: every recursively enumerable set of natural numbers is Diophantine. We present the formalization of Matiyasevich’s proof of the DPRM theorem in Isabelle. To represent recursively enumerable sets in equations, we implement and arithmetize register machines. Using several number-theoretic lemmas, we prove that exponentiation has a diophantine representation. Further, we contribute a small library of number-theoretic implementations of binary digit-wise relations. Finally, we discuss and contribute an is_diophantine predicate. We expect the complete formalization of the DPRM theorem in the near future; at present it is complete except for a minor gap in the arithmetization proofs of register machines and extending the is_diophantine predicate by two binary digit-wise relations.
Cite as

Jonas Bayer, Marco David, Abhik Pal, Benedikt Stock, and Dierk Schleicher. The DPRM Theorem in Isabelle (Short Paper). In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 33:1-33:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{bayer_et_al:LIPIcs.ITP.2019.33,
  author =	{Bayer, Jonas and David, Marco and Pal, Abhik and Stock, Benedikt and Schleicher, Dierk},
  title =	{{The DPRM Theorem in Isabelle}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{33:1--33:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.33},
  URN =		{urn:nbn:de:0030-drops-110883},
  doi =		{10.4230/LIPIcs.ITP.2019.33},
  annote =	{Keywords: DPRM theorem, Hilbert’s tenth problem, Diophantine predicates, Register machines, Recursively enumerable sets, Isabelle, Formal verification}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.11
Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

Authors: Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel

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

Abstract
We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below epsilon-0. In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes. Our formal library also provides, somewhat nonstandardly, multisets with negative multiplicities and syntactic ordinals with negative coefficients. We present applications of the library to formalizations of Goodstein's theorem and the decidability of unary PCF (programming computable functions).
Cite as

Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel. Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{blanchette_et_al:LIPIcs.FSCD.2017.11,
  author =	{Blanchette, Jasmin Christian and Fleury, Mathias and Traytel, Dmitriy},
  title =	{{Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{11:1--11:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.11},
  URN =		{urn:nbn:de:0030-drops-77155},
  doi =		{10.4230/LIPIcs.FSCD.2017.11},
  annote =	{Keywords: Multisets, ordinals, proof assistants}
}
  • Refine by Author
  • 2 Fleury, Mathias
  • 1 Bayer, Jonas
  • 1 Bentkamp, Alexander
  • 1 Biere, Armin
  • 1 Blanchette, Jasmin Christian
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Automated reasoning
  • 1 Computing methodologies → Theorem proving algorithms
  • 1 Theory of computation → Higher order logic

  • Refine by Keyword
  • 1 DPRM theorem
  • 1 DRAT
  • 1 Diophantine predicates
  • 1 FRAT
  • 1 Formal verification
  • Show More...

  • Refine by Type
  • 4 document

  • Refine by Publication Year
  • 1 2017
  • 1 2019
  • 1 2020
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact