end if Clause Samples
The 'end if' clause serves as a marker to indicate the conclusion of a conditional statement in programming or scripting languages. It is used to clearly define where the block of code governed by an 'if' condition ends, ensuring that only the intended statements are executed when the condition is met. By explicitly marking the end of a conditional block, this clause helps prevent logical errors and enhances code readability, making it easier to maintain and debug complex scripts.
end if. Algorithm 1: Implementing ND-broadcast in BAMPn,t[t < n/3] When a process pi wants to ND-broadcast a message whose content is vi, it broadcasts the message ND INIT(i, vi) (line 1). When a process receives a message ND INIT(j, −) for the first time, it broad- casts a message ND ECHO(j, v) where v is the data content of the ND INIT() message (line 2). If the message ND INIT(j, v) received is not the first message ND INIT(j, −), pj is Byzantine and the message is discarded. Finally, when pi has received the same message ND ECHO(j, v) from (n − t) different processes, it locally ND-delivers MSG(j, v) (lines 3-4). The algorithm considers an instance of ND-broadcast, i.e., a correct process invokes at most once ND-broadcast. Adding a sequence number to each message allows each process to ND-broadcast a sequence of messages.
Theorem 1. Algorithm 1 implements ND-broadcast in the system model BAMPn,t[t < n/3]. 1A similar vocabulary will be used for the abstractions MV-broadcast and SMV-broadcast introduced in Section 3. Proof To prove the ND-termination property, let us consider a non-faulty process pi that ND-broadcasts the message MSG(vi). As pi is non-faulty, the message ND INIT(i, vi) is received by all the non-faulty processes, which are at least (n − t), and every non-faulty process broadcasts ND ECHO(i, vi) (line 2). Hence, each non-faulty process receives the message ND ECHO(i, vi). from (n − t) different processes. It follows that every non-faulty process eventually ND-delivers the message MSG(i, vi) (lines 3-4). To prove the ND-no-duplicity property, let us assume by contradiction that two non-faulty processes pi and pj ND-deliver different messages m1 and m2 from some process pk (i.e., m1 = MSG(k, v) and m2 = MSG(k, w), with v /= w). It follows from the predicate of line 3, that pi received ECHO(k, v) from a set of (n − t) distinct processes, and pj received ECHO(k, w) from a set of (n − t) distinct processes. As n > 3t, it follows that the intersection of these two sets contains a non-faulty process. But, as it is non-faulty, this sent the same message ND ECHO() to pi and pj (line 2). Hence, m1 = m2, which contradicts the initial assumption. To prove the ND-validity property, we show that, if Byzantine processes forge and broadcast a message ND ECHO(i, w) such that pi is correct and has never invoked ND broadcast MSG(w), then no correct process can ND-deliver MSG(i, w). Let us observe that at most t processes can broadcast the message ND ECHO(i, w). As ...
end if. Network participants perform faultCorr(·) Ui−1 performs sendSK(·) function