This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position's delta at each point in time over an infinite time horizon, thus taking into account the perpetual nature and optionality to withdraw of liquidity provision. This framework yields two key theoretical results: (a) It proves that the AMM's adverse-selection cost, loss-versus-rebalancing (LVR), is analytically identical to the continuous funding fees (the time value decay or theta) earned by the at-the-money CI option embedded in the replicating portfolio. (b) A special case of this model derives an AMM liquidity position's delta profile and boundaries that suffer approximately constant LVR, up to a bounded residual error, over an arbitrarily long forward window. Finally, the paper describes how the constant volatility parameter required by the perpetual option can be calibrated from the term structure of implied volatilities and estimates the errors for both implied volatility calibration and LVR residual error. Thus, this work provides a practical framework enabling liquidity providers to choose an AMM liquidity profile and price boundaries for an arbitrarily long, forward-looking time window where they can expect an approximately constant, price-independent LVR. The results establish a rigorous option-theoretic interpretation of AMMs and their LVR, and provide actionable guidance for liquidity providers in estimating future adverse-selection costs and optimizing position parameters.

This paper investigates the current state of option trading platforms for cryptocurrencies, encompassing both centralized and decentralized exchanges. Option contracts in cryptocurrency markets offer functionalities akin to traditional markets, providing investors with tools to mitigate risks, particularly those arising from price volatility. The paper discusses these applications of option contracts in the context of decentralized finance, emphasizing their utility in managing market uncertainties. Despite a recent surge in the trading volume of option contracts on cryptocurrencies, decentralized platforms account for less than $1 \%$ of this total volume. Hence, this paper takes a closer look by examining the design choices of these platforms to understand the challenges hindering their growth and adoption. It identifies technical, financial, and adoption-related challenges faced by decentralized exchanges. Subsequently, the paper provides commentary on existing platform responses.

This paper introduces BAKUP, a smart contract design that insures decentralized finance users against the vulnerability risks in third-party platforms. Apart from providing an automated claim payout, the modular structure of BAKUP brings harmonization among three conflicting features: resilience against vulnerabilities, flexibility of the underwritten policies, and capital efficiency. An immutable core module performs basic accounting while ensuring robustness against external vulnerabilities; a customizable oracle module enables the underwriting of novel policies, and a peripheral (optional) yield module allows users to independently manage additional yield without interfering with the risk management of fellow participants. User payoff is implemented using binary conditional ERC20 tokens tradable on automated market maker (AMM)-based exchanges.

We present the Layered Merkle Patricia Trie (LMPT), a performant storage data structure for processing transactions in high-throughput systems when compared to traditional Merkle Patricia Tries used in Ethereum clients. LMPTs keep smaller intermediary tries in memory to alleviate read and write amplification from high-latency disk storage. As an additional feat, they also allow for the I/O and transaction verifier threads to be scheduled in parallel and independently. LMPTs can ultimately reduce significant I/O traffic that happens on the critical path of transaction processing. Empirical results show that LMPTs can process up to$\times6$more transactions per second on real-life ERC20 smart contract workloads when compared to existing Ethereum clients.

This paper presents Mobius, the first cost-efficient state sharding design that remains consensus mechanism agnostic and guarantees atomicity for cross-shard smart contract transactions. In particular, to address the challenges posed by the growing blockchain state, Mobius enables its participants to verify all transactions while only storing a partial state. Unlike previous state sharding systems, the proposed protocol uses a novel vector commitment data structure to reduce the network bandwidth overhead via proof aggregation. Further, it utilizes a novel epoch-based multi-phase commitment technique for guaranteeing atomicity in cross-shard transactions. Experiments presented here show that Mobius reduces the disk requirement of each participant linearly with respect to the number of shards. Further, it presents a 4.7-7.3x lower network bandwidth overhead when compared to existing state-of-the-art state sharding systems. The outcomes also confirm that existing smart contracts can operate on Mobius in cross-shard scenarios without modifications.

This paper presents Deeper, a design for a decentralized exchange that enhances the average active liquidity via reserve sharing. By doing this, it addresses the problem of shallow liquidity in low trading volume token pairs. Deeper allows liquidity providers of multiple trading pairs against a common token to share liquidity. This is achieved by creating a common reserve pool for the shared token that is accessible by each trading pair. Independent from the shared liquidity, providers are free to add liquidity to individual token pairs without any restriction. The trading between one token pair does not affect the price of other token pairs even though the reserve of the shared token changes. The proposed design is an extension of concentrated liquidity market maker-based DEXs that is simple enough to be implemented on smart contracts. Experiments show that for a batch consisting of 8 trading pairs, Deeper enhances liquidity by over 2.6 − 5.9 ×. This enhancement in liquidity can be increased further by increasing participating tokens in the shared pool.

Neural Networks have long been a mainstream technique to solve optimization problems. A classic example is the Travelling Salesman Problem (TSP) which NP-hard. Using a Hopfield-Tank representation, an n-city problem is mapped to a cost function of n2interacting neural units. Stochastic gradient descent helps achieve the global minima. Due to the nature of the TSP problem, the cost function has to penalize invalid sub-routes (non-Hamiltonian cycles) and minimize the travel cost simultaneously. In addition, there is a starting point and travel direction associated `2n' degeneracy. Previously, a cellular neuronal approach was proposed where the neural units were replaced with oscillators. The phase relations determined the output solution. Multiphase clusters of these oscillators solved the degeneracy issue. This paper proposes an n-oscillator cost function for an n -city TSP. Since a group of single frequency oscillator phases are naturally ordered and circular in a system, the proposed method exploits the true potential of oscillator nodes. The sub-routes and degeneracy are eliminated by design in addition to massively increasing the scaling potential (n vs. n2). It was also found that the proposed n- mapping can converge to the optimum tour much faster (about 100 times for a 5-city problem) than for n2mapping. Our approach projects hardware efficiency in terms of area footprint, computation time and energy. With coupled single device-based compact nanoscale oscillator systems becoming increasingly viable in hardware, efficient cost function mappings of hard problems using oscillator phases, as shown here, is critical to solving large graphical optimization problems.