Common use of Fault Handling Clause in Contracts

Fault Handling. Every player p maintains a player list Lp and adds to it in each round all players he reliably detects to be faulty. This list of detected players will never contain any correct player. Let p be a correct player. In order to nd conditions for the detection of faulty players by p, we rst derive a condition that must be satis ed for every internal node of the IG-tree corresponding to a correct player. Let r be an internal node corresponding to a correct player r. During information gathering, r distributes the same value treer( ) = v for his node to every player. Accordingly, in the following round, only a faulty player q may send to p a distinct value w = v for Finally, after n 3 + 1 runs, either all faulty players have been globally his node r. Hence there exists an adversary set A and a unique value v detected or Byzantine agreement has been achieved. If we let every correct player such that all players q with treep( rq) = v are covered by X. Xxxxxxxx, the set of already detected players Lp must be a subset of such an A, i.e. the condition 992A f2 x x[ : A ( c C( r) treep( rc) = v Lp) is satis ed. Hence player r can be reliably detected to be faulty by player p if there is no such value v. This rule can be applied during information gathering: player p adds player r to Lp if there is no such value v. By Lemma 2, this even holds for the converted values of r's child nodes. Hence we can apply the same rule for the resolved 5 A player does not necessarily know which of the players he detected are globally detected and which are not. Fault detectio[nfdugring in9form:atiofn2gatherinjg (FD1): g[ values as well and we obtain the following fault detection rules to be applied by player p for every internal node r: Lp := Lp r if

Fault Handling. Every player p maintains a player list Lp and adds to it in each round all players he reliably detects to be faulty. This list of detected players will never contain any correct player. Let p be a correct player. In order to nd conditions for the detection of faulty players by p, we rst derive a condition that must be satis ed for every internal node of the IG-tree corresponding to a correct player. Let r be an internal node corresponding to a correct player r. During information gathering, r distributes the same value treer( ) = v for his node to every player. Accordingly, in the following round, only a faulty player q may send to p a distinct value w = 6= v for Finally, after n 3 + 1 runs, either all faulty players have been globally his node r. Hence there exists an adversary set A 2 A and a unique value v detected or Byzantine agreement has been achieved. If we let every correct player such that all players q with treep( rq) = 6= v are covered by X. XxxxxxxxA. Moreover, the set of already detected players Lp must be a subset of such an A, i.e. the condition 992A f2 x x[ 9v : 9A 2 A : A ( c (fc 2 C( r) j treep( rc) = v 6= vg[ Lp) is satis ed. Hence player r can be reliably detected to be faulty by player p if there is no such value v. This rule can be applied during information gathering: player p adds player r to Lp if there is no such value v. By Lemma Xxxxx 2, this even holds for the converted values of r's child nodes. Hence we can apply the same rule for the resolved 5 A player does not necessarily know which of the players he detected are globally detected and which are not. Fault detectio[nfdugring in9form:atiofn2gatherinjg (FD1): g[ values as well and we obtain the following fault detection rules to be applied by player p for every internal node r: Lp Fault detection during information gathering (FD1): p p p p L := L [ frg if 69v : :Q1(fc 2 C( r) j tree ( rc) 6= vg[ L ): Fault detection during data conversion (FD2): p p p p L := L [ frg if 69v : :Q1(fc 2 C( r) j resolve ( rc) 6= vg[ L ): Fault Masking: After a player r has been added to the list Lp by player p in some communication round k, then every message by player r ifin round k and any subsequent round is replaced by the default value 0. Once a player has been globally detected (by all correct players), he will be masked to send the same values to all correct players. Thus, every node r for which a value is received after player r's global detection will be common. We are ready to summarize the complete protocol (the description is given for the view by player p).

Fault Handling. Every player p maintains a player list Lp and adds to it in each round all players he reliably detects to be faulty. This list of detected players will never contain any correct player. Let p be a correct player. In order to nd conditions for the detection of faulty players by p, we rst derive a condition that must be satis ed for every internal node of the IG-tree corresponding to a correct player. Let r be an internal node corresponding to a correct player r. During information gathering, r distributes the same value treer( ) = v for his node to every player. Accordingly, in the following round, only a faulty player q may send to p a distinct value w = 6= v for Finally, after n 3 + 1 runs, either all faulty players have been globally his node r. Hence there exists an adversary set A 2 A and a unique value v detected or Byzantine agreement has been achieved. If we let every correct player such that all players q with treep( rq) = 6= v are covered by X. XxxxxxxxA. Moreover, the set of already detected players Lp must be a subset of such an A, i.e. the condition 992A f2 x x[ 9v : 9A 2A : A ( c (fc 2 C( r) j treep( rc) = v 6= vg[ Lp) is satis ed. Hence player r can be reliably detected to be faulty by player p if there is no such value v. This rule can be applied during information gathering: player p adds player r to Lp if there is no such value v. By Lemma 2, this even holds for the converted values of r's child nodes. Hence we can apply the same rule for the resolved 5 A player does not necessarily know which of the players he detected are globally detected and which are not. Fault detectio[nfdugring in9form:atiofn2gatherinjg (FD1): g[ values as well and we obtain the following fault detection rules to be applied by player p for every internal node r: Lp Fault detection during information gathering (FD1): p p p p L := L [ frg if 69v : :Q1(fc 2 C( r) j tree ( rc) 6= vg[ L ): Fault detection during data conversion (FD2): p p p p L := L [ frg if 69v : :Q1(fc 2 C( r) j resolve ( rc) 6= vg[ L ): Fault Masking: After a player r has been added to the list Lp by player p in some communication round k, then every message by player r ifin round k and any subsequent round is replaced by the default value 0. Once a player has been globally detected (by all correct players), he will be masked to send the same values to all correct players. Thus, every node r for which a value is received after player r's global detection will be common. We are ready to summarize the complete protocol (the description is given for the view by player p).

Fault Handling. Every player p maintains a player list Lp and adds to it in each round all players he reliably detects to be faulty. This list of detected players will never contain any correct player. Let p be a correct player. In order to nd conditions for the detection of faulty players by p, we rst derive a condition that must be satis ed for every internal node of the IG-tree corresponding to a correct player. Let r be an internal node corresponding to a correct player r. During information gathering, r distributes the same value treer( ) = v for his node to every player. Accordingly, in the following round, only a faulty player q may send to p a distinct value w = v for Finally, after n 3 + 1 runs, either all faulty players have been globally his node r. Hence there exists an adversary set A and a unique value v detected or Byzantine agreement has been achieved. If we let every correct player such that all players q with treep( rq) = v are covered by X. Xxxxxxxx, the set of already detected players Lp must be a subset of such an A, i.e. the condition 992A f2 x x[ : A ( c C( r) treep( rc) = v Lp) is satis ed. Hence player r can be reliably detected to be faulty by player p if there is no such value v. This rule can be applied during information gathering: player p adds player r to Lp if there is no such value v. By Lemma 2, this even holds for the converted values of r's child nodes. Hence we can apply the same rule for the resolved 5 A player does not necessarily know which of the players he detected are globally detected and which are not. Fault detectio[nfdugring in9form:atiofn2gatherinjg (FD1): g[ values as well and we obtain the following fault detection rules to be applied by player p for every internal node r: Lp := Lp r if