With the continuous development of the blockchain industry, Layer 2 has been gradually launched for the market public. At the same time, the expansion solutions for Layer 0 and Layer 1 are also being continuously optimized. From Layer 0 to Layer 2, the most essential difference lies in the realization of the state channel. Next, in this article, we will use mathematical theory to outline the difference between the realization of the state channel from Layer 0 to ayer 2.
Author: Seth V
Source: Medium
Compiler: Chen Yiwanfeng
We will use isomorphic (isomorphic) that is Cardano's Hydra Layer 2 state channel, and hylomorphic (alien) that is Constellation's Layer 0 State channel as an example, explain the difference between the implementation of the state channel from Layer 0 to ayer 2, and explore its far-reaching impact on interoperability and scalability.
What is isomorphic?
Basically, isomorphic allows one data type to be mathematically mapped to another different data type in order to retain basic information, and can be expressed and referenced in different systems for other mathematical operations and representations . This is what Cardano is doing to ensure the validity and integrity of the atomic exchange between its Layer 1 ledger and its Layer 2 isomorphic state channel.
Cardano regards their Layer 1 as the settlement layer, and Layer 2 as the computing layer for extended transactions and smart contracts. By using isomorphic state channels, Cardano essentially expands the Layer 1 network in an organic way, avoiding the need to create bridges in an independent Layer 2 network, which requires packaging of native assets and Plutus smart contracts, which is a big trouble. Most Ethereum Layer 2 problems.
What is Hylomorphism?
What Constellation does is to create a data type system,The system can use high-dimensional category theory and homotopy theory to mathematically abstract data types into generalized algebraic geometry topology. This level of mathematical abstraction allows the "Layer 0" meta-network to mathematically model the data types and structures contained in data streams generated from external networks and systems (such as Layer 1 and Layer 2 networks or private enterprise and government systems).
This means that you can map morphisms to morphisms with mathematical origins, which allows a hierarchy of complex data types to be formed and represented as geometric space in a directed acyclic graph. Because the data is stored in this way, it is essentially given the attributes of a physical object, which can be used to observe the information state in it, thereby forming a consensus in a unique way:
The above figure can be regarded as two The dimensional information is transposed into a three-dimensional space, similar to the computational geometry mathematics used by 3D code engines (Unity, Unreal, etc.) to generate textures and surfaces in video games. In this case, the data is immutable, can contain almost any data type that the state channel wants to verify, and does not require a graphics card or the like, because you are not actually rendering the graphics. This example shows that the basic theory of mathematical space can contain a variety of concepts, including matrices, vector spaces, and manifolds.
manifolds allow complex structures to be described by the easy-to-understand topological properties of simple spaces, making them easier to interact. This technique is used to model the physical surface of an object in geometry, and it can also be used to model data as a mathematical surface. Tessellation is another technique mentioned by Wyatt for reasoning about surfaces, which allows the surface to be split into smaller subsets that fit together to generate computer graphics.
In general, it is studied as a "point set topology" or "general topology" with various branches, including differentiation, geometry, and algebra. Constellation Network can even use it to observe how all these geometric spaces are related to each other in time (represented as the fourth dimension)... because space and time (that is, time and space in the theory of relativity) are mathematically bound to each other , It can perform asynchronous verification of concurrent events:
This is done using a series of Catamorphisms (folding),These Catamorphisms (folding) decompose a larger structure into a reduced value ("cata" stands for "down"), and Anamorphisms (expanding), which build a structure from a set of smaller values ("ana") as ("Up"). And this also successfully created a Hylomorphism, which is a transformation after a reverse shape in the sequence of technical operations.
Please refer to the figure below and the corresponding folding and unfolding operations, which produces the so-called "Hylochain":
"Hylochain" is basically an information tree, which can compare different data without losing any data. The information is mathematically compressed and decompressed, and the information will not be classified into a simple low-level type system.
Wyatt Meldman-Floch’s white paper details Constellation’s unique computational geometry framework, which creates this mathematical topology to formally define the primitives of the distributed ledger, and uses probabilistic algebraic abstractions to create static types. The meta-protocol of the metalanguage to define the boundaries between agreements.
combined with the use of the Java/Scala programming language makes it very easy to represent and formally verify information from external off-chain data sources (such as another blockchain network or some IT database system) without changing the underlying layer data structure. Due to the microservice architecture and the asynchronous consensus in each state channel, Constellation has unlimited scalability while converging to the global asynchronous Hypergraph state.
Because Constellation has the ability to handle complex data structures, it can map the Cardano data type to the direct acyclic graph in Hypergraph to represent it. However, Cardano only develops their state channels to process their extended UTXO The data type of the transaction. It cannot be configured like Constellation's state channel logic, nor does it have the flexibility to define a custom consensus standard.Their Hydra protocol is an isomorphic state channel. Technically speaking, it is a directed acyclic graph that can process and verify transactions asynchronously and concurrently, but it cannot abstract data types beyond this range
, which is Said that the Hydra protocol is very impressive. In theory, each Hydra head can be expanded to one million transactions. So far, all state channel solutions are limited by the date types supported by their scripting language and smart contract logic, such as Raiden Network (Ethereum) and Lightning Network (Bitcoin).
Layer 0 is inclusive, not exclusivity
By summarizing the differences between the state channels of Layer 0 to Layer 2, we understand how they interoperate together to take advantage of each other. By letting Cardano integrate the Layer 2 Hydra state channel into the Layer 0 Constellation state channel, it extends its ecosystem to a multi-chain network that shares the same mathematical integrity values provided by functional programming and formal verification. This will enable Cardano to access a truly decentralized and interoperable liquidity order book, and allow its Dapp and integration with SingularityNet’s AI agent to gain greater access through Constellation’s meta-network Hypergraph Transfer Protocol (HGTP) Customer network.
Of course, this integration can be extended to any Layer 1 or Layer 2 network, not just the Cardano state channel.
As an industry, realizing the value of a social vision has always been a goal. In this vision, we can inject the qualities of immutability, transparency, security and personal sovereignty into the transaction that reshapes the modern world. system.If we want to upgrade to Social 3.0, which we are all eagerly awaiting, we need to jointly develop a strategy to execute its technical implementation.
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