by *Xavier Llorà (2006).* IlliGAL TR No 2006017. Link to the PDF.

**Abstract**

This technical report describes how to compute the fitness of a rule for an arbitrary size multiplexer without doing any instance matching. Pittsburgh-style learning classifier systems require the *accuracy* and the *error* of a rule to compute a fitness that promotes maximally accurate and maximally general rules. The *accuracy* (α) may be computed as the proportion of overall examples correctly classified, and the *error* (ε) is the proportion of incorrect classifications issued. Once the *accuracy* and *error* of a rule are known, the fitness can be computed as *f(r)=α(r)*ε(r)*. This technical note shows how to computed the fitness only by inspecting the rule, requiring a time proportional to number of possible address values *O(2^|a|)* instead of the *O(2^l)* that requires a traditional rule matching strategy against all the possible instances. The proposed method makes tractable for Pittsburgh learning classifier systems multiplexer problems larger than the 11-input one.