Yaron Velner

Krishnendu Chatterjee, Amir Kafshdar Goharshady, Rasmus Ibsen-Jensen et al.

Crypto-currencies are digital assets designed to work as a medium of exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest behavior of participants). A framework for the analysis of attacks in crypto-currencies requires (a) modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior; (b) concurrent interactions between participants; and (c) analysis of long-term monetary gains. Traditional game-theoretic approaches for the analysis of security protocols consider either qualitative temporal properties such as safety and termination, or the very special class of one-shot (stateless) games. However, to analyze general attacks on protocols for crypto-currencies, both stateful analysis and quantitative objectives are necessary. In this work our main contributions are as follows: (a) we show how a class of concurrent mean-payoff games, namely ergodic games, can model various attacks that arise naturally in crypto-currencies; (b) we present the first practical implementation of algorithms for ergodic games that scales to model realistic problems for crypto-currencies; and (c) we present experimental results showing that our framework can handle games with thousands of states and millions of transitions.

Yaron Velner

Mean-payoff games play a central role in quantitative synthesis and verification. In a single-dimensional game a weight is assigned to every transition and the objective of the protagonist is to assure a non-negative limit-average weight. In the multidimensional setting, a weight vector is assigned to every transition and the objective of the protagonist is to satisfy a boolean condition over the limit-average weight of each dimension, e.g., $\LimAvg(x_1) \leq 0 \vee \LimAvg(x_2)\geq 0 \wedge \LimAvg(x_3) \geq 0$. We recently proved that when one of the players is restricted to finite-memory strategies then the decidability of determining the winner is inter-reducible with Hilbert's Tenth problem over rationals (a fundamental long-standing open problem). In this work we allow arbitrary (infinite-memory) strategies for both players and we show that the problem is undecidable.