Discovering Functional Formulas through Changing Representation Base

This paper deals with computer generation of numerical functional formulas describing results of scientific experiments (measurements). It describes the methodology for generating functional physical laws called COPER (Kokar 1985a). This method generates only so called "meaningful functions", i.e., such that fulfill some syntactic conditions. In the case of physical laws these conditions are described in the theory of dimensional analysis, which provides rules for grouping arguments of a function into a (smaller) number of dimensionless monomials. These monomials constitute new arguments for which a functional formula is generated. COPER takes advantage of the fact that the grouping is not unique since it depends on which of the initial arguments are chosen as so called "dimensional base" (representation base). For a given functional formula the final result depends on the base. In its search for a functional formula COPER first performs a search through different representation bases for a fixed form of the function before going into more complex functional formulas. It appears that for most of the physical laws only two classes of functional formulas linear functions and second degree polynomials need to be considered to generate a formula exactly matching the law under consideration.