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A. Appendix, ?. .. {1, and ?. , V M ) of M values from some domain D. It supports two operations ; scan() takes no parameter and returns the value of V , and update(i,x ), writes x to the i-th component of V and returns nothing. Our implementation uses an array A[1 . . . M ] of shared registers and a register S. Each array entry A[i] stores a triple (w i , p i , b i ), where w i ? D represents the i-th entry in the vector V of the snapshot object, p i is a process ID or ? which identifies the last process that wrote to A[i], and b i ? {0, 1} is a bounded (modulo 2) sequence number. Initially, S = ? and each array entry A[i] has the value (w i , ?, 0) for some fixed w i ? D. Now suppose process p calls update(i, x), and this is p's j-th update of the i-th component of V

. Hence, ); in particular it writes the triple (w, q, b) to A[i] at some point t * ? (t 1 , t 2 ) Recall that each time q writes to A[i] it alternates the bit it writes to the third component. Hence, at no point in [t 1 , t * ] the second and third component of A[i] can have value q and b