THE EIG STRUCTURE AND RULES Sample Clauses

THE EIG STRUCTURE AND RULES. In this section we define the EIG structure and rules. | | ⊥ ∈ Let N be the set of processes, n = N and assume that n > 3t. Let D be a set of possible decision values. We assume some decision D is the designated default deci- sion. Let Σr be the set of all sequences of length r of elements of S N without repetition. Let Σ0 = g, the empty sequence. Let Property 1. When the protocol is invoked, no correct process appears in the faulty sets of any other correct process. Moreover, p p and p q for any two correct processes p and q, T| FA | ≥ − FA ⊆ F FA ⊆ F Each invocation of the EIG protocol is tagged with a pa- rameter φ, known to all processes. An EIG protocol with parameter φ, will run for at most φ+1 rounds. At the begin- ning of the agreement protocol the faulty sets are empty at all correct processes and the EIG protocol with parameter φ = t is executed. Each additional invocation of the EIG protocol is with a smaller value of φ. In the non-trivial case, when the EIG protocol with parameter φ is invoked then i i t φ. There will be one exception to this as- sumption, and it is handled in Lemma 1. Thus, other than in that specific case, it is assumed that we have a (t, φ)- adversary during the execution of the EIG protocol with parameter φ. The basic EIG protocol for a correct process z with initial value dz ∈ D is very simple: IT IT