eth2.0-specs/specs/core/0_fork-choice.md

Ethereum 2.0 Phase 0 -- Beacon Chain Fork Choice

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

Table of contents

• Ethereum 2.0 Phase 0 -- Beacon Chain Fork Choice
  • Table of contents
  • Introduction
  • Constants
    • Time parameters
  • Beacon chain processing
    • Beacon chain fork choice rule

Introduction

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

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.previous_block_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 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] returns 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].high_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)))