Authors: Marinković, Bojan 
Glavan, Paola
Ognjanović, Zoran 
Doder, Dragan
Studer, Thomas
Title: Probabilistic consensus of the blockchain protocol
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 11726 LNAI
First page: 469
Last page: 480
Conference: 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2019; Belgrade; Serbia; 18 September 2019 through 20 September 2019
Issue Date: 1-Jan-2019
Rank: M33
ISBN: 978-3-030-29764-0
ISSN: 0302-9743
DOI: 10.1007/978-3-030-29765-7_39
We introduce a temporal epistemic logic with probabilities as an extension of temporal epistemic logic. This extension enables us to reason about properties that characterize the uncertain nature of knowledge, like “agent a will with high probability know after time s same fact”. To define semantics for the logic we enrich temporal epistemic Kripke models with probability functions defined on sets of possible worlds. We use this framework to model and reason about probabilistic properties of the blockchain protocol, which is in essence probabilistic since ledgers are immutable with high probabilities. We prove the probabilistic convergence for reaching the consensus of the protocol.
Keywords: Blockchain | Formal model | Multi-agent systems | Specification/verification | Temporal epistemic logic with probabilities
Publisher: Springer Link
Project: Mathematical Modelas and Optimization Methods on Large-Scale Systems 
Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Swiss National Science Foundation

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