Adaptive Random Testing with Combinatorial Input Domain

Table 2

Similarity measures for categorical parameter values.

Measure	𝑆𝑖(𝑋𝑖,𝑌𝑖)	𝜔𝑖,𝑖=1,2,…,𝑘	Range
Goodall1	=1−𝑞∈𝑄𝑝^2𝑖(𝑞)if𝑋𝑖=𝑌𝑖0otherwise	1𝑘	20,1−𝑁^2; [0,0]
Goodall2	=1−𝑞∈𝑄𝑝^2𝑖(𝑞)if𝑋𝑖=𝑌𝑖0otherwise	1𝑘	21−𝑁^2,1; [0,0]
Goodall3	=1−𝑝^2𝑖(𝑋𝑖)if𝑋𝑖=𝑌𝑖0otherwise	1𝑘	10,1−𝑁^2; [0,0]
Goodall4	=𝑝^2𝑖(𝑋𝑖)if𝑋𝑖=𝑌𝑖0otherwise	1𝑘	[1𝑁^2,1]; [0,0]
Lin	=2log𝑝𝑖(𝑋𝑖)if𝑋𝑖=𝑌𝑖2log(𝑝𝑖(𝑋𝑖)+𝑝𝑖(𝑌𝑖))otherwise	1∑^𝑘𝑖=1log𝑝𝑖(𝑋𝑖)+log𝑝𝑖(𝑌𝑖)	[−2log𝑁,0]; 𝑁−2log2,0
Lin1	=^𝑞∈𝑄log𝑝𝑘(𝑞)if𝑋𝑖=𝑌𝑖2log𝑞∈𝑄𝑝𝑘(𝑞)otherwise	1∑^𝑘𝑖=1∑𝑞∈𝑄log𝑝𝑖(𝑋𝑖)	[−𝑁log𝑁,0]; 𝑁[−2log2,0]
Overlap	=1if𝑋𝑖=𝑌𝑖0otherwise	1𝑘	[1,1]; [0,0]
Eskin	=1if𝑋𝑖=𝑌𝑖𝑉𝑖^2𝑉𝑖^2+2otherwise	1𝑘	[1,1]; 23,𝑁^2𝑁^2+2
OF	=1if𝑋𝑖=𝑌𝑖11+log𝑁/𝑓𝑖(𝑋𝑖)×log𝑁/𝑓𝑖(𝑌𝑖)otherwise	1𝑘	[1,1]; 11+(log𝑁)^2,11+(log2)^2

Note. For measure Goodall1, 𝑄={𝑞∣𝑞∈𝑉_𝑖,𝑝_𝑖(𝑞)≥𝑝_𝑖(𝑋_𝑖)}.
For measure Goodall2, 𝑄={𝑞∣𝑞∈𝑉_𝑖,𝑝_𝑖(𝑞)≤𝑝_𝑖(𝑋_𝑖)}.
For measure Lin1, 𝑄={𝑞∣𝑞∈𝑉_𝑖,min(𝑝_𝑖(𝑋_𝑖),𝑝_𝑖(𝑌_𝑖))≤𝑝_𝑖(𝑞)≤max(𝑝_𝑖(𝑋_𝑖),𝑝_𝑖(𝑌_𝑖))}.