A note on the independence number, domination number and related parameters of random binary search trees and random recursive trees

We identify the mean growth of the independence number of random binary search trees and random recursive trees and show normal fluctuations around their means. Similarly we also show normal limit laws for the domination number and variations of it for these two cases of random tree models. Our results are an application of a recent general theorem of Holmgren and Janson on fringe trees in these two random tree models

SoK: Blockchain Decentralization

Blockchain empowers a decentralized economy by enabling distributed trust in a peer-to-peer network. However, surprisingly, a widely accepted definition or measurement of decentralization is still lacking. We explore a systematization of knowledge (SoK) on blockchain decentralization by comprehensively analyzing existing studies in various aspects. First, we establish a taxonomy for analyzing blockchain decentralization in the five facets of consensus, network, governance, wealth, and transaction. We find a lack of research on the transaction aspects that closely characterize user behavior. Second, we apply Shannon entropy in information theory to propose a decentralization index for blockchain transactions. We show that our index intuitively measures levels of decentralization in peer-to-peer transactions by simulating blockchain token transfers. Third, we apply our index to empirically analyze the dynamics of DeFi token transfers by three methods of description, prediction, and causal inference. In the descriptive analysis, we observe that levels of decentralization converge inter-temporally, regardless of the initial levels. A comparative study across DeFi applications shows that exchange and lending are more decentralized than payment and derivatives across DeFi applications. Second, in the predictive analysis, we also discover that a greater return of Ether, the native coin of the Ethereum blockchain, predicts a greater transaction decentralization in stablecoin that include Ether as collateral. Third, in an event study of causal inference, we find the change of Ethereum Transaction Fee Mechanism to EIP-1559 significantly changes the decentralization level of DeFi transactions. Finally, we identify future research directions

Provably Secure Decisions based on Potentially Malicious Information

There are various security-critical decisions routinely made, on the basis of information provided by peers: routing messages, user reports, sensor data, navigational information, blockchain updates, etc. Jury theorems were proposed in sociology to make decisions based on information from peers, which assume peers may be mistaken with some probability. We focus on attackers in a system, which manifest as peers that strategically report fake information to manipulate decision making. We define the property of robustness: a lower bound probability of deciding correctly, regardless of what information attackers provide. When peers are independently selected, we propose an optimal, robust decision mechanism called Most Probable Realisation (MPR). When peer collusion affects source selection, we prove that generally it is NP-hard to find an optimal decision scheme. We propose multiple heuristic decision schemes that can achieve optimality for some collusion scenarios

Why factors facilitating collusion may not predict cartel occurrence — experimental evidence

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordFactors facilitating collusion may not successfully predict cartel occurrence: When a factor predicts that collusion (explicit and tacit) becomes easier, firms might be less inclined to set up a cartel simply because tacit coordination already tends to go in hand with supra‐competitive profits. We illustrate this issue with laboratory data. We run n‐firm Cournot experiments with written cheap‐talk communication between players and we compare them to treatments without the possibility to talk. We conduct this comparison for two, four, and six firms. We find that two firms indeed find it easier to collude tacitly but that the number of firms does not significantly affect outcomes with communication. As a result, the payoff gain from communication increases with the number of firms, at a decreasing rate

Blockchain Trilemma Solver Algorand has Dilemma over Undecidable Messages

Recently, an ingenious protocol called Algorand has been proposed to overcome these limitations. Algorand uses an innovative process - called cryptographic sortition - to securely and unpredictably elect a set of voters from the network periodically. These voters are responsible for reaching consensus through a Byzantine Agreement (BA) protocol on one block per time, guaranteeing an overwhelming probability of linearity of the blockchain. In this paper, we present a security analysis of Algorand. To the best of our knowledge, it is the first security analysis as well as the first formal study on Algorand. We designed an attack scenario in which a group of malicious users tries to break the protocol, or at least limiting it to a reduced partition of network users, by exploiting a possible security flaw in the messages validation process of the BA. Since the source code or an official simulator for Algorand was not available at the time of our study, we created a simulator (which is available on request) to implement the protocol and assess the feasibility of our attack scenario. Our attack requires the attacker to have a trivial capability of establishing multiple connections with targeted nodes and costs practically nothing to the attacker. Our results show that it is possible to slow down the message validation process on honest nodes, which eventually forces them to choose default values on the consensus; leaving the targeted nodes behind in the chain as compared to the non-attacked nodes. Even though our results are subject to the real implementation assumption, the core concept of our attack remains valid.Comment: 8 pages, 2 figures, and 2 table