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Table 3:
Summary of statistical analysis of XCSCFA, XCSF, and XCSSMA in learning different Boolean problems. The methods in the “Best Performance” column are significantly better than the methods in the “Worst Performance” column. Two methods in the same cell are not significantly different.
Problem DomainProblem SizeBest PerformanceWorst Performance
Multiplexer 6-bit No significant difference No significant difference 
 11-bit No significant difference No significant difference 
 20-bit XCSCFA, XCSSMA XCSF 
 37-bit XCSCFA XCSF 
 70-bit XCSF XCSCFA 
Majority-on 7-bit XCSCFA, XCSSMA XCSF 
 9-bit XCSCFA, XCSSMA XCSF 
 11-bit XCSSMA XCSF 
Carry 4+4 bit No significant difference No significant difference 
 5+5 bit XCSCFA, XCSSMA XCSF 
 6+6 bit XCSSMA XCSF 
 n+n bit Only XCSSMA generated applicable solutions Only XCSSMA generated applicable solutions 
Even-parity 7-bit XCSSMA XCSF 
 8-bit XCSSMA XCSF 
 9-bit XCSSMA XCSF 
 24-bit XCSSMA XCSCFA, XCSF 
 n-bit Only XCSSMA generated applicable solutions Only XCSSMA generated applicable solutions 
Count ones 7-bit XCSCFA, XCSSMA XCSF 
 9-bit XCSCFA XCSF 
DV1 7-bit XCSCFA, XCSSMA XCSF 
Problem DomainProblem SizeBest PerformanceWorst Performance
Multiplexer 6-bit No significant difference No significant difference 
 11-bit No significant difference No significant difference 
 20-bit XCSCFA, XCSSMA XCSF 
 37-bit XCSCFA XCSF 
 70-bit XCSF XCSCFA 
Majority-on 7-bit XCSCFA, XCSSMA XCSF 
 9-bit XCSCFA, XCSSMA XCSF 
 11-bit XCSSMA XCSF 
Carry 4+4 bit No significant difference No significant difference 
 5+5 bit XCSCFA, XCSSMA XCSF 
 6+6 bit XCSSMA XCSF 
 n+n bit Only XCSSMA generated applicable solutions Only XCSSMA generated applicable solutions 
Even-parity 7-bit XCSSMA XCSF 
 8-bit XCSSMA XCSF 
 9-bit XCSSMA XCSF 
 24-bit XCSSMA XCSCFA, XCSF 
 n-bit Only XCSSMA generated applicable solutions Only XCSSMA generated applicable solutions 
Count ones 7-bit XCSCFA, XCSSMA XCSF 
 9-bit XCSCFA XCSF 
DV1 7-bit XCSCFA, XCSSMA XCSF 
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