Distributed Sequential Consensus in Networks: Analysis of Partially Connected Blockchains with Uncertainty

Table 1

Evolution of states in the transaction graph shown in Figure 1(b) obtained by iterating (1) steps for (a) and (b) orderings. The initial state is and . The order relationship induces the double spending effect.

(a)

0	1	1	0	0	0
1	0	1	1	0	0
2	0	1	0	1	0
3	0	0	1	1	0
4	0	0	0	1	1

(b)

0	1	1	0	0	0
1	0	1	1	0	0
2	0	1	0	1	0
3	0	1	−1	1	1
4	0	0	0	1	1