Search for: All records

Many aspects of blockchain-based decentralized finance can be understood as an extension of classical distributed computing. In this paper, we trace the evolution of two interrelated notions: failure and fault-tolerance. In classical distributed computing, a failure to complete a multi-party protocol is typically attributed to hardware malfunctions. A fault-tolerant protocol is one that responds to such failures by rolling the system back to an earlier consistent state. In the presence of Byzantine failures, a failure may be the result of an attack, and a fault-tolerant protocol is one that ensures that attackers will be punished and victims compensated. In modern decentralized finance however, failure to complete a protocol can be considered a legitimate option, not a transgression. A fault-tolerant protocol is one that ensures that the party offering the option cannot renege, and the party purchasing the option provides fair compensation (in the form of a fee) to the offering party. We sketch the evolution of such protocols, starting with two-phase commit, and finishing with timed hashlocked smart contracts. 

Automated market makers (AMMs) are automata that trade electronic assets at rates set by mathematical formulas.AMMs are usually implemented by smart contracts on blockchains. In practice, AMMs are often composed: trades can be split across AMMs, and outputs from one AMM can be directed to another. This paper proposes a mathematical model for AMM composition. We define sequential and parallel composition operators for AMMs in a way that ensures that AMMs are closed under composition, in a way that works for “higher-dimensional” AMMs that manage more than two asset classes, and so the composition of AMMs in “stable” states remains stable.