Recognition of Whitehead-Minimal Elements in Free Groups of Large Ranks - Artificial Intelligence and Symbolic Computation - page 218

Table 1. Description of the training and test datasets in free groups F 10 , F 15 and F 20 .

Dataset size %min%non-min(min,avg,max) word lengths

D 20000 49.1 50.9 (3,558.2,1306)

S e

5000 48.9 51.1 (3,559,1292)

S 10 5000 49.1 50.9 (3,1016.5,13381)

S R 5000 98.3 1.7 (3,501.2,999)

S P 3850 0.0 100.0 (3,194.7,8719)

a) F 3 ;

Dataset size %min%non-min(min,avg,max) word lengths

D 20000 48.5 51.5 (5,581.3,1388)

S e 5000 49.2 50.8 (8,583.7,1382)

S 10 5000 48.0 52.0 (7,1693.22,28278)

S R 5000 97.2 2.8 (6,504.2,999)

S P 2900 0.0 100.0 (5,656.9,22430)

c) F 5 ;

Dataset size %min%non-min(min,avg,max) word lengths
D

9660 48.9 51.1 (26,617.4,1461)

S e 4811 49.2 50.8 (26,619.7,1443)

S 10 4837 49.5 50.5 (29,2589.8,65274)

S R 4867 96.5 3.5 (18,512.7,999)

S P

165 0.0 100.0 (12,150.8,1459)

a) F 10 ;

Dataset size %min%non-min(min,avg,max) word lengths
D 9357 49.5 50.5 (41,635.3,1472)

S e 4685 49.2 50.8 (40,642.5,1462)

S 10 4722 49.7 50.3 (46,3056.6,53422)

S R

4755 95.3 4.7 (26,523.8,999)

S P 870 0.0 100.0 (28,1109.3,4981)

b) F 15 ;

Dataset size %min%non-min(min,avg,max) word lengths
D

9144 49.6 50.4 (47,658.3,1488)

S e 4576 49.3 50.7 (48,659.8,1484)

S 10 4597 49.1 50.9 (64,3351.4,68316)

S R 4643 94.0 6.0 (48,534.9,999)

S P 182 0.0 100.0 (66,945.1,4762)

c) F 20 ;

4.2 Accuracy Measure
To evaluate the performance of the classification system PR MIN we define an
accuracy measure A .