Named arguments for checkAdversarialRecipe

Image of checkAdversarialRecipe when it accepts the recipe

Image of checkAdversarialRecipe when it rejects the recipe

See CheckedAdversarialRecipe

Reject a bad AdversarialRecipe

Generate an adversarial ChainSchema that satifies checkExtendedRaceAssumption

The distribution this function samples from is not simple to describe. It begins by drawing a sample of length adv from the Bernoulli process induced by the active slot coefficient Asc. (IE adv many i.i.d. samples from Uniform(f)). Then it visits the Extended Praos Race Windows that overlap with the prefix of that leader schedule that ends one stability window after the first (remaining) active adversarial slot in it. In each such Window, it removes the youngest active slots from the adversarial leader schedule until it loses that Race.

Finally, it ensures that the density of the alternative schema is less than the density of the honest schema in the first stability window after the intersection.

The leader schedule of an honest chain

The represented chain grows by one block per active slot. A different data type would represent a leader schedule in which leaders do not necessarily extend the block from the previous active slot.

INVARIANT: at least one active slot

A violation of Races Before Acceleration Assumption

INVARIANT: windowLast rvAdv < windowLast rvHon + Delta

INVARIANT: windowStart rvHon <= windowStart rvAdv

Check the chain matches the given AdversarialRecipe.

• It must intersect the honest chain at an active slot
• It must satisfy the Races Before Acceleration Assumption (which implies the Length of Competing Chains Assumption)

Definition of a Praos Race Window of a chain. It is an interval of slots that contains at least k+1 blocks of the chain and exactly Delta slots after the k+1st block.

Definition of the Length of Competing Chains Assumption. We assume every adversarial chain contains at most k blocks in the Praos Race Window anchored at the the intersection.

Definition of Acceleration Lower Bound of an Adversarial Chain. It is the lowest slot at which an adversary could speed up its elections on a given adversarial chain. It is defined as the Scg-th slot after the first adversarial block or the Delta-th slot after the k+1st honest block after the intersection, whichever is greater.

Definition of the Races Before Acceleration Assumption. Every adversarial chain has at most k blocks in every Praos Race Window of the honest chain that starts after the intersection and ends before the acceleration lower bound.

Definition of the Genesis Implication Conjecture. We conjecture that assuming that the Genesis window length is no greater than the Stability Window and that every possible adversarial chain satisfies the Races in Stability Windows Assumption, then the honest chain strictly wins every possible density comparison from the Ouroboros Genesis paper. The key intuition is that a less dense chain would have to lose at least one Praos race within the Genesis window.

Draw a random active slot count for the prefix of a fork.

The result is guaranteed to leave more than k active slots after the intersection in the honest and the adversarial chains. See Note [Minimum schema length] in Test.Ouroboros.Consensus.ChainGenerator.Honest for the rationale of the precondition.

PRECONDITION: schemaSize schedH >= s + d + k + 1