Blockchain Cohomology

MACSPro'2019 - Modeling and Analysis of Complex Systems and Processes, Vienna
21 - 23 March 2019

Wyatt Meldman-Floch

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Transcript

1. Blockchain Cohomology: MapReduce models for Blockchain technology Wyatt Meldman-Floch March 22, 2019
2. Background • Data Engineer ◦ Distributed systems & Machine Learning • Cofounder and CTO of Constellation • API/Data pipeline security • Data validation • Core technology: Blockchain for big data
3. • Consensus protocol ◦ Data with correctness guarantees • Secure tamper proof log ◦ Measurable via computational cost of forging cryptographic key signatures • Decentralized code execution ◦ Repurpose consensus protocol to perform action based on state transition Blockchain Evolution: Transactions -> Digital contracts -> Applications Bitcoin Ethereum
4. Blockchain limitations • Finite block sizes and single block validation, or single network partitions • Waste resources, redundant work • Different networks cannot connect • Centralized platform lock-in • Can’t start your own network • Low throughput • GDPR and legal compliance • Secure interaction of smart contract api - Unsolved
5. NonLinear Protocols: Applications • Concurrent consensus ◦ eventually consistent consensus ◦ Light nodes for IoT and Edge computing ◦ Secure code execution in parallel and across channels
6. State of the industry • In the akward phase ◦ Tools exist for many specific use cases, lacking interoperation standards • Reminiscent of big data space ~10 years ago ◦ MapReduce was a success, but programs were brittle and
7. MapReduce’s scalability • MapReduce is a framework for highly concurrent data processing ◦ Its most scalable attribute is its high level API ◦ Abstract low level data locality management and allow application developers to focus on business logic
8. If it worked before... • Treat like a distributed data set ◦ Application logic removed from data locality • What about topological data? ◦ Recursion schemes = typesafe gather apply scatter ◦ Types connect the feature space
9. Hylomorphism = MapReduce • Hylo = anamorphism + catamorphism ◦ Batch operations • Metamorphism = catamorphism + anamorphism ◦ Stream processing • Inverses of each other ◦ And this is reflected algebraically!
10. Functoral operators • Monadic execution context ◦ Reactive/microservice architectures
11. Category theory ⇔ Functional programming • Translate complex behavior to high level abstractions • Verify code correspondance to analytical models • Functions are proofs • F(unctor)-Algebra ◦ Defines an api as a typed functoral operation • F-coAlgebra ◦ Defines how to mix different APIs, implicitly
12. Recursion Schemes: Nature’s high level api • Call(back) tree ◦ Allows us to define a protocol in terms of maps and reduces across other protocols
13. The Constellation problem • Eventually consistent (horizontally scalable) • Reward nodes for optimizing network topology. • Subscriber based data validation • Reputation bases consensus model Stochastic neural gas: topology finding algorithm
14. • Constellation produces hierarchical edges • Hierarchies are an efficient way of handling data locality: storing subsets of the data dependency graph to minimize network traffic (latency). • Scale free network π 1 π 2 π 3 π 4 π n πn πn- 1 πn-1 πn-1 Constellation: How data is stored
15. Chain Complex Model • Omega: ◦ Parent type • Epsilon: ◦ Data type of “child” blocks • T: ◦ Topology • Gamma: ◦ Total state space
16. Use Case: Sharding/side channel mechanisms • Outer product of epsilon gives total space • Monadic execution context ◦ Reactive/microservice architectures Layer 2 - eg Lightning Sharding - eg Zilliqa
17. Use Case: State channels • Vector space representation • Many node/IoT systems ◦ End to end security • Topological data analysis ◦ Online neural networks ◦ Computer vision ◦ Edge computing 0 1 a 1 b 2 3 b 3 a Translation: .reduceByKey()
18. Takeaways • API call graphs can be mapped over • Types verify distributed systems • Distributed systems verified and designed with algebraic models • We can use these models to validate topological data