Mainly regarding Resources spent per Tx Processing
At Node Level
Cost of Validation
Cost of Consensus (PoW, PoS, ...)
At Blockchain Level
How much of the computation is replicated across the nodes
Design
Having a state model which relies on a canonical global state only, means having no parallelization at all
In global state context, Block adding is a Blockchain wide synchronization point hence it slows up computation
Furthermore, Consensus like PoW make this event even slower in order to make it both expensive and random
The idea is scaling performance by improving the parallelization at state model level, which introduces the idea of decoherence (relaxing the vinculus of evolving the BC state machine by global states only)
Think about the Actor Model : each Blockchain is an actor which runs its own processing independently and in parallel with the respect to the other Actors, Polkadot provides essentially a Decentralized Message Passing Framework
More Scalability is achieved by increasing Parallelism
Elements
Relay Chain: the Polkadot Core
Parachains (Parallel Blockchains): Blockchain connecting to Polkadot = Actors
Bridges: allow to connect to Blockchain with their own Consensus
Focusing on Distributed Computation only (so considering Decentralization and Trustless Context at a later stage) there are 2 fundamental needs: Distributed Communication and Standardized Computation
Distributed Communication
Requirements
Needs to be P2P
Needs to provide enough flexibility to implement a huge amount of higher level protocols
Needs to be computationally efficient as it is focused on running on multiple devices, with different HW and available resources in general (e.g. bandwidth, battery, …)
Needs to guarantee any operation gives the same result independently on the underlying computational infrastructure hence providing a full abstraction layer
Needs to standardize the computation cost even considering a high level measurement unity (e.g. Ethereum Gas) : e.g. a certain operation needs to cost X gas independently of the platform
-- Similar to C++ Specs specifying the computational complexity of operations on containers
Read Through and Analysis of the Polkadot Whitepaper