Analysis and Application of Transition Systems Based on Petri Nets and Relation Matrices to Business Process Management

Table 2

The key nodes for each trace of log L₁ in Algorithm 2.

Trace	Node	Current state	Prefix alignment	Current cost
σ1		([p1], s0)	<>	0
		([p2], sa)	<(a, t1)>	0
		([p3], )	<(a, t1), (b, t2)>	0
		([p4], )	<(a, t1), (b, t2), (>>, t4)>	1
σ2		([p1], s0)	<>	0
		([p2], s0)	<(>>, t1)>	1
		([p3], )	<(>>, t1), (b, t2)>	1
		([p4], )	<(>>, t1), (b, t2), (d, t4)>	1
σ3		([p1], s0)	<>	0
		([p2], sa)	<(a, t1)>	0
		([p2], sa)	<(a, t1), (a, >>)>	1
		([p3], )	<(a, t1), (a, >>), (b, t2)>	1
		([p4], )	<(a, t1), (a, >>), (b, t2), (>>, t4)>	2
σ4		([p1], s0)	<>	0
		([p2], sa)	<(a, t1)>	0
		([p3], )	<(a, t1), (b, t2)>	0
		([p4], )	<(a, t1), (b, t2), (d, t4)>	0