% % % Purpose : properties of the communication system passing exact information % and operating in a fault-full environment. % % %
exact_comm
[
N : [nat -> posnat],
T : TYPE+
] : THEORY
BEGIN
IMPORTING
node_functions[N, T],
exact_comm_stage
i, j, k: VAR nat
sources: VAR [j : nat -> finite_set[below(N(j))]]
sent: VAR sent_vec
rcvd: VAR rcvd_matrix
check: VAR check_function
tau: VAR [i: nat -> tau_type]
% % Abstracted fault assumptions %
% same predicate is in inexact_comm
enabled_within?(rcvd, check, j, k)(sources): bool = FORALL i : j <= i AND i < k IMPLIES
enabled_within?[N(i), N(i + 1), T](rcvd(i), check(i))(sources(i))
% For every stage between j..k, and at every receiver, there is a % quorum (simple majority or more) of source nodes that exhibit correct communication
quorum_correct?(sent, rcvd, check, tau, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
quorum_correct?[N(i), N(i+1), T](sent(i), rcvd(i), check(i), tau(i))
% For every stage between j..k, and at every receiver, there is a % majority of source nodes that exhibit correct communication
majority_correct?(sent, rcvd, check, j, k): bool = FORALL i : j <= i AND i < k IMPLIES
majority_correct?[N(i), N(i+1), T](sent(i), rcvd(i), check(i))
% For some stage i (j<=i<k), there is a set of nodes % that exhibits only symmetric communication. Furthermore, % a quorum (simply majority or more) are correct for % all subsequent stages
exists_all_symmetric?(sent, rcvd, check, tau, j, k): bool = EXISTS i: j <= i AND i < k AND
all_symmetric?(rcvd(i), check(i)) AND
quorum_correct?(sent, rcvd, check, tau, i+1, k)
% exists_all_symmetric?(sent, rcvd, check, j, k): bool = % EXISTS i: j <= i AND i < k AND % all_symmetric?(rcvd(i), check(i)) AND % majority_correct?(sent, rcvd, check, i+1, k)
% Specialization for the simple majority case.
exists_all_symmetric?(sent, rcvd, check, j, k): bool =
exists_all_symmetric?(sent, rcvd, check, mid, j, k)
END exact_comm
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