Stake Shift in Major Cryptocurrencies: An Empirical Study

In the proof-of-stake (PoS) paradigm for maintaining decentralized, permissionless cryptocurrencies, Sybil attacks are prevented by basing the distribution of roles in the protocol execution on the stake distribution recorded in the ledger itself. However, for various reasons this distribution cannot be completely up-to-date, introducing a gap between the present stake distribution, which determines the parties' current incentives, and the one used by the protocol. In this paper, we investigate this issue, and empirically quantify its effects. We survey existing provably secure PoS proposals to observe that the above time gap between the two stake distributions, which we call stake distribution lag, amounts to several days for each of these protocols. Based on this, we investigate the ledgers of four major cryptocurrencies (Bitcoin, Bitcoin Cash, Litecoin and Zcash) and compute the average stake shift (the statistical distance of the two distributions) for each value of stake distribution lag between 1 and 14 days, as well as related statistics. We also empirically quantify the sublinear growth of stake shift with the length of the considered lag interval. Finally, we turn our attention to unusual stake-shift spikes in these currencies: we observe that hard forks trigger major stake shifts and that single real-world actors, mostly exchanges, account for major stake shifts in established cryptocurrency ecosystems.Comment: 20 pages, 8 figures, 2 tables, paper accepted for publication at Financial Cryptography and Data Security 2020 (FC 2020, see https://fc20.ifca.ai

A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

Optimal Reachability for Multi-Priced Timed Automata

AbstractIn this paper, we prove the decidability of the minimal and maximal reachability problems for multi-priced timed automata, an extension of timed automata with multiple cost variables evolving according to given rates for each location. More precisely, we consider the problems of synthesizing the minimal and maximal costs of reaching a given target location. These problems generalize conditional optimal reachability, i.e., the problem of minimizing one primary cost under individual upper bound constraints on the remaining, secondary, costs, and the problem of maximizing the primary cost under individual lower bound constraints on the secondary costs. Furthermore, under the liveness constraint that all traces eventually reach the goal location, we can synthesize all costs combinations that can reach the goal.The decidability of the minimal reachability problem is proven by constructing a zone-based algorithm that always terminates while synthesizing the optimal cost tuples. For the corresponding maximization problem, we construct two zone-based algorithms, one with and one without the above liveness constraint. All algorithms are presented in the setting of two cost variables and then lifted to an arbitrary number of cost variables