Ethereum 2.0 Phase 0 -- Beacon Chain Fork Choice

Notice: This document is a work-in-progress for researchers and implementers.

Ethereum 2.0 Phase 0 -- Beacon Chain Fork Choice

Introduction

This document represents the specification for the beacon chain fork choice rule, part of Ethereum 2.0 Phase 0.

Prerequisites

All terminology, constants, functions, and protocol mechanics defined in the Phase 0 -- The Beacon Chain doc are requisite for this document and used throughout. Please see the Phase 0 doc before continuing and use as a reference throughout.

Constants

Time parameters

Name	Value	Unit	Duration
`SECONDS_PER_SLOT`	`6`	seconds	6 seconds

Beacon chain processing

Processing the beacon chain is similar to processing the Ethereum 1.0 chain. Clients download and process blocks and maintain a view of what is the current "canonical chain", terminating at the current "head". For a beacon block, block, to be processed by a node, the following conditions must be met:

The parent block with root block.parent_root has been processed and accepted.
An Ethereum 1.0 block pointed to by the state.latest_eth1_data.block_hash has been processed and accepted.
The node's Unix time is greater than or equal to state.genesis_time + block.slot * SECONDS_PER_SLOT.

Note: Leap seconds mean that slots will occasionally last SECONDS_PER_SLOT + 1 or SECONDS_PER_SLOT - 1 seconds, possibly several times a year.

Note: Nodes needs to have a clock that is roughly (i.e. within SECONDS_PER_SLOT seconds) synchronized with the other nodes.

Beacon chain fork choice rule

The beacon chain fork choice rule is a hybrid that combines justification and finality with Latest Message Driven (LMD) Greediest Heaviest Observed SubTree (GHOST). At any point in time, a validator v subjectively calculates the beacon chain head as follows.

Abstractly define Store as the type of storage object for the chain data, and let store be the set of attestations and blocks that the validator v has observed and verified (in particular, block ancestors must be recursively verified). Attestations not yet included in any chain are still included in store.
Let finalized_head be the finalized block with the highest epoch. (A block B is finalized if there is a descendant of B in store, the processing of which sets B as finalized.)
Let justified_head be the descendant of finalized_head with the highest epoch that has been justified for at least 1 epoch. (A block B is justified if there is a descendant of B in store the processing of which sets B as justified.) If no such descendant exists, set justified_head to finalized_head.
Let get_ancestor(store: Store, block: BeaconBlock, slot: Slot) -> BeaconBlock be the ancestor of block with slot number slot. The get_ancestor function can be defined recursively as:

def get_ancestor(store: Store, block: BeaconBlock, slot: Slot) -> BeaconBlock:
    """
    Get the ancestor of ``block`` with slot number ``slot``; return ``None`` if not found.
    """
    if block.slot == slot:
        return block
    elif block.slot < slot:
        return None
    else:
        return get_ancestor(store, store.get_parent(block), slot)

Let get_latest_attestation(store: Store, index: ValidatorIndex) -> Attestation be the attestation with the highest slot number in store from the validator with the given index. If several such attestations exist, use the one the validator v observed first.
Let get_latest_attestation_target(store: Store, index: ValidatorIndex) -> BeaconBlock be the target block in the attestation get_latest_attestation(store, index).
Let get_children(store: Store, block: BeaconBlock) -> List[BeaconBlock] return the child blocks of the given block.
Let justified_head_state be the resulting BeaconState object from processing the chain up to the justified_head.
The head is lmd_ghost(store, justified_head_state, justified_head) where the function lmd_ghost is defined below. Note that the implementation below is suboptimal; there are implementations that compute the head in time logarithmic in slot count.

def lmd_ghost(store: Store, start_state: BeaconState, start_block: BeaconBlock) -> BeaconBlock:
    """
    Execute the LMD-GHOST algorithm to find the head ``BeaconBlock``.
    """
    validators = start_state.validator_registry
    active_validator_indices = get_active_validator_indices(validators, slot_to_epoch(start_state.slot))
    attestation_targets = [(i, get_latest_attestation_target(store, i)) for i in active_validator_indices]

    # Use the rounded-balance-with-hysteresis supplied by the protocol for fork
    # choice voting. This reduces the number of recomputations that need to be
    # made for optimized implementations that precompute and save data
    def get_vote_count(block: BeaconBlock) -> int:
        return sum(
            start_state.validator_registry[validator_index].effective_balance
            for validator_index, target in attestation_targets
            if get_ancestor(store, target, block.slot) == block
        )

    head = start_block
    while 1:
        children = get_children(store, head)
        if len(children) == 0:
            return head
        # Ties broken by favoring block with lexicographically higher root
        head = max(children, key=lambda x: (get_vote_count(x), hash_tree_root(x)))

Implementation notes

Justification and finality at genesis

During genesis, justification and finality root fields within the BeaconState reference ZERO_HASH rather than a known block. ZERO_HASH in previous_justified_root, current_justified_root, and finalized_root should be considered as an alias to the root of the genesis block.

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