Dynamic Piecewise Function Reconstruction on Blockchain Consensus

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Solution Overview

Problem

In peer-to-peer computing environments, especially on blockchain systems, computing piecewise functions is inefficient due to the need for consensus algorithms in distributed systems lacking trust, leading to increased computational overhead.

Innovation Solution

The implementation of a system and method that determines regions on curve functions and anchor reserve values to optimize the computation of piecewise linear functions, reducing computational complexity by pre-computing expensive operations and using parameterization, allowing for efficient redemption of stablecoins in a blockchain system.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If piecewise functions are computed on blockchain systems with consensus algorithms, then trust and reliability are improved, but computational overhead and time are significantly increased

Engineering Contradiction:

ImprovetrustVSAvoidcomputational overhead

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent pre-computes and stores piecewise function definitions, anchor points, and region boundaries in the blockchain state before transactions occur. This allows nodes to retrieve pre-computed data during transaction processing, eliminating the need for real-time complex computations while maintaining consensus trust.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent segments the curve function into multiple linear regions defined by anchor points and boundaries. Each region can be independently queried and processed, reducing the computational burden on individual transactions while maintaining the overall integrity of the piecewise function through distributed consensus.

Inventive Principle:

Principle #1Segmentation

2Productivity

If piecewise functions are simplified for computation, then computational efficiency is improved, but accuracy and precision may be reduced

Engineering Contradiction:

Improvecomputational efficiencyVSAvoidaccuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent applies different levels of precision to different regions of the piecewise function based on local requirements. Each linear region can be independently optimized for computation while maintaining sufficient accuracy for its specific domain, allowing computational efficiency without sacrificing overall precision.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The patent changes the representation parameters of the curve function by using anchor points and linear segment definitions instead of complex mathematical functions. This parameter transformation enables efficient linear computations while preserving the accuracy of the original non-linear function through careful selection of anchor points.

Inventive Principle:

Principle #35Parameter changes

3Productivity

If conventional computing systems are used for piecewise functions, then computational efficiency is improved, but adaptability to distributed trust environments is reduced

Engineering Contradiction:

Improvecomputational efficiencyVSAvoidadaptability to distributed trust environments

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent designs a universal piecewise function representation that works both in centralized and distributed environments. The same anchor point and linear region structure can be used in conventional systems for efficiency and in blockchain systems with consensus algorithms for trust, providing adaptability across different computing paradigms.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent introduces the piecewise function structure as an intermediary layer between the mathematical model and the computing system. This intermediary representation can be efficiently evaluated in conventional systems while being verifiable and consensually agreed upon in distributed blockchain environments, bridging the gap between efficiency and trust.

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS20230362020A1Systems and methods for reconstructing and computing dynamic piecewise functions on distributed consensus systems

Publication Date: 2023.11.09 SUPERLUMINAL LABS LTD

AI summary

A system for implementing an algorithmic market maker is configured to: receive a transaction including a request to redeem an amount of stablecoins for a reserve asset; retrieve initial states of a current block of a blockchain; determine a region on a curve function associating the stablecoin and the reserve asset, the curve function including at least two regions; determine an anchor reserve value based at least in part on the determined region; and provide a redemption amount of the reserve asset in exchange for the amount of stablecoins in the request based at least in part on the anchor reserve value.