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DOI: 10.4230/LIPIcs.CP.2024.9

Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms

Authors: Emir Demirović, Ciaran McCreesh, Matthew J. McIlree, Jakob Nordström, Andy Oertel, and Konstantin Sidorov

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract

Pseudo-Boolean proof logging has been used successfully to provide certificates of optimality from a variety of constraint- and satisifability-style solvers that combine reasoning with a backtracking or clause-learning search. Another paradigm, occurring in dynamic programming and decision diagram solving, instead reasons about partial states and possible transitions between them. We describe a framework for generating clean and efficient pseudo-Boolean proofs for these kinds of algorithm, and use it to produce certifying algorithms for knapsack, longest path, and interval scheduling. Because we use a common proof system, we can also reason about hybrid solving algorithms: we demonstrate this by providing proof logging for a dynamic programming based knapsack propagator inside a constraint programming solver.

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Emir Demirović, Ciaran McCreesh, Matthew J. McIlree, Jakob Nordström, Andy Oertel, and Konstantin Sidorov. Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{demirovic_et_al:LIPIcs.CP.2024.9,
  author =	{Demirovi\'{c}, Emir and McCreesh, Ciaran and McIlree, Matthew J. and Nordstr\"{o}m, Jakob and Oertel, Andy and Sidorov, Konstantin},
  title =	{{Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.9},
  URN =		{urn:nbn:de:0030-drops-206948},
  doi =		{10.4230/LIPIcs.CP.2024.9},
  annote =	{Keywords: Proof logging, dynamic programming, decision diagrams}
}

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DOI: 10.4230/LIPIcs.CP.2023.26

Proof Logging for Smart Extensional Constraints

Authors: Matthew J. McIlree and Ciaran McCreesh

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

Proof logging provides an auditable way of guaranteeing that a solver has produced a correct answer using sound reasoning. This is standard practice for Boolean satisfiability solving, but for constraint programming, a challenge is that every propagator must be able to justify all inferences it performs. Here we demonstrate how to support proof logging for a wide range of previously uncertified global constraints. We do this by showing how to justify every inference that could be performed by the propagation algorithms for two families of generalised extensional constraint: "Smart Table" and "Regular Language Membership".

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Matthew J. McIlree and Ciaran McCreesh. Proof Logging for Smart Extensional Constraints. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mcilree_et_al:LIPIcs.CP.2023.26,
  author =	{McIlree, Matthew J. and McCreesh, Ciaran},
  title =	{{Proof Logging for Smart Extensional Constraints}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.26},
  URN =		{urn:nbn:de:0030-drops-190633},
  doi =		{10.4230/LIPIcs.CP.2023.26},
  annote =	{Keywords: Constraint programming, proof logging, extensional constraints}
}

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Pseudo-Boolean Reasoning About States and Transitions to Certify Dynamic Programming and Decision Diagram Algorithms

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Proof Logging for Smart Extensional Constraints

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