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Datei: exact_comm.pvs Sprache: PVS

Original von: PVS^©

%
%
% 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))

  mid(i): tau_type = mid

  majority_correct_rw: LEMMA
    majority_correct?(sent, rcvd, check, j, k) IFF
      quorum_correct?(sent, rcvd, check, mid, j, k)

  % 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

¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤

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