Bonding Curve Segmentation for Smart Contract Efficiency
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Solution Overview
Problem
Integrating bond curves in smart contracts is an expensive operation due to their ill-suitedness for complex mathematical processing, particularly involving hypergeometric functions that lack a closed form and require series summation.
Innovation Solution
Approximating the bonding curve using multiple curve segments with simpler functions, such as polynomials and exponential terms, that have closed-form integrals, allowing for easier integration and computation, and updating the curve segments based on constraints to maintain the desired shape and pool balance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a bonding curve defined by hypergeometric functions is used in a smart contract, then the price-supply relationship can be accurately maintained, but the computational cost and complexity increase significantly
Solution Approach 1:
The bonding curve is divided into multiple curve segments, each defined by simpler functions (polynomials, exponentials) that have closed-form integrals. These segments concatenate to approximate the overall bonding curve shape, replacing the single complex hypergeometric function with multiple manageable pieces that are computationally efficient to evaluate and integrate.
Solution Approach 2:
The patent transforms the bonding curve from a complex hypergeometric function to a piecewise definition using parameters that control the shape and position of curve segments. By changing the mathematical representation parameters, the system maintains the essential bonding curve behavior while using computationally simpler functions that smart contracts can efficiently process.
2Reliability
If hypergeometric functions are used to define the bonding curve, then the price-supply relationship is maintained, but series summation is required which is expensive for smart contracts
Solution Approach 1:
The bonding curve is segmented into multiple pieces, each with a closed-form integral. This eliminates the need for series summation that would be required for hypergeometric functions, as each segment can be integrated directly using standard mathematical operations that are computationally inexpensive for smart contracts.
Solution Approach 2:
The patent replaces expensive hypergeometric function evaluations with cheaper alternative functions (polynomials, exponentials) that have closed-form integrals. These simpler functions are computationally inexpensive to evaluate and integrate, making them suitable for the resource-constrained environment of smart contracts.
3Device complexity
If multiple curve segments are used to approximate the bonding curve, then computational costs are reduced, but the curve approximation accuracy must be maintained
Solution Approach 1:
The bonding curve is divided into multiple curve segments that concatenate to form the complete curve. Each segment is defined by simple functions with closed-form integrals, and together they approximate the desired bonding curve shape. The segmentation allows for both computational efficiency and adequate accuracy through proper choice of segment count and parameters.
Solution Approach 2:
The patent uses parameters to control the shape, position, and smoothness of curve segments. By adjusting these parameters, the system achieves an optimal balance between the number of segments (affecting computational complexity) and the accuracy of the curve approximation, ensuring that the simplified segments closely match the original bonding curve behavior.
Data Source
Figure 1a~1c
Figure 2
Figure 3a~3b
AI summary
Some embodiments are directed to a computer-implemented method for maintaining crypto tokens of a first type. A smart contract from a distributed ledger defines a bonding curve being as a sequence of multiple curve segments. A creation or annul function of the smart contract may integrate a bonding curve starting from the current supply size to a new supply size to determine an amount of crypto tokens of a second type. The crypto tokens of the second type may be transferred to or from a pool associated with the smart contract, while crypto tokens of the first type may be transferred to a user or may be destroyed. The current supply size of first type tokens may be updated correspondingly.