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Documents authored by Beckmann, Arnold

Document
DOI: 10.4230/LIPIcs.MFCS.2024.21
On Complexity of Confluence and Church-Rosser Proofs

Authors: Arnold Beckmann and Georg Moser

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In this paper, we investigate confluence and the Church-Rosser property - two well-studied properties of rewriting and the λ-calculus - from the viewpoint of proof complexity. With respect to confluence, and focusing on orthogonal term rewrite systems, our main contribution is that the size, measured in number of symbols, of the smallest rewrite proof is polynomial in the size of the peak. For the Church-Rosser property we obtain exponential lower bounds for the size of the join in the size of the equality proof. Finally, we study the complexity of proving confluence in the context of the λ-calculus. Here, we establish an exponential (worst-case) lower bound of the size of the join in the size of the peak.
Cite as

Arnold Beckmann and Georg Moser. On Complexity of Confluence and Church-Rosser Proofs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beckmann_et_al:LIPIcs.MFCS.2024.21,
  author =	{Beckmann, Arnold and Moser, Georg},
  title =	{{On Complexity of Confluence and Church-Rosser Proofs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.21},
  URN =		{urn:nbn:de:0030-drops-205774},
  doi =		{10.4230/LIPIcs.MFCS.2024.21},
  annote =	{Keywords: logic, bounded arithmetic, consistency, rewriting}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2021.1
Verification of Bitcoin Script in Agda Using Weakest Preconditions for Access Control

Authors: Fahad F. Alhabardi, Arnold Beckmann, Bogdan Lazar, and Anton Setzer

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract
This paper contributes to the verification of programs written in Bitcoin’s smart contract language script in the interactive theorem prover Agda. It focuses on the security property of access control for script programs that govern the distribution of Bitcoins. It advocates that weakest preconditions in the context of Hoare triples are the appropriate notion for verifying access control. It aims at obtaining human-readable descriptions of weakest preconditions in order to close the validation gap between user requirements and formal specification of smart contracts. As examples for the proposed approach, the paper focuses on two standard script programs that govern the distribution of Bitcoins, Pay to Public Key Hash (P2PKH) and Pay to Multisig (P2MS). The paper introduces an operational semantics of the script commands used in P2PKH and P2MS, which is formalised in the Agda proof assistant and reasoned about using Hoare triples. Two methodologies for obtaining human-readable descriptions of weakest preconditions are discussed: (1) a step-by-step approach, which works backwards instruction by instruction through a script, sometimes grouping several instructions together; (2) symbolic execution of the code and translation into a nested case distinction, which allows to read off weakest preconditions as the disjunction of conjunctions of conditions along accepting paths. A syntax for equational reasoning with Hoare Triples is defined in order to formalise those approaches in Agda.
Cite as

Fahad F. Alhabardi, Arnold Beckmann, Bogdan Lazar, and Anton Setzer. Verification of Bitcoin Script in Agda Using Weakest Preconditions for Access Control. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 1:1-1:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alhabardi_et_al:LIPIcs.TYPES.2021.1,
  author =	{Alhabardi, Fahad F. and Beckmann, Arnold and Lazar, Bogdan and Setzer, Anton},
  title =	{{Verification of Bitcoin Script in Agda Using Weakest Preconditions for Access Control}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{1:1--1:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.1},
  URN =		{urn:nbn:de:0030-drops-167704},
  doi =		{10.4230/LIPIcs.TYPES.2021.1},
  annote =	{Keywords: Blockchain, Cryptocurrency, Bitcoin, Agda, Verification, Hoare logic, Bitcoin Script, P2PKH, P2MS, Access control, Weakest precondition, Predicate transformer semantics, Provable correctness, Symbolic execution, Smart contracts}
}
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