On the complexity of polarized polynomials of functions of many-valued logics that depend on one variable

We consider multi-valued logic functions represented by polarised polynomials. A polynomial is called polarised if each its variable can be polarised by a certain shift. We introduce the Shannon function which characterises the complexity of representations of multi-valued logic functions by polarised polynomials and obtain an exact estimate of the Shannon function for functions in one variable.
This research was supported by the Russian Foundation for Basic Research, grant 00–01–00351.