\input zb-basic
\input zb-ioport
\iteman{io-port 01775542}
\itemau{Pogosyan, Grant R.}
\itemti{Classes of Boolean functions defined by functional terms.}
\itemso{Mult.-Valued Log. 7, No.5-6, 417-448 (2001).}
\itemab
A way to define classes of Boolean functions by certain expressions called functional terms is introduced. It is an extension of a system that uses identities, presented by {\it O. Ekin}, {\it S. Foldes}, {\it P. L. Hammer} and {\it L. Hellerstein} [Discrete Math. 211, 27-51 (2000; Zbl 0947.06008)]. Although the two schemes are equivalent in expressive power, the new approach has a number of advantages. The main results include a general characterization of term-definable classes in terms of certain closure properties. In particular, it follows that any clone of Boolean functions is term-definable. On the other hand, the family of term-definable classes is shown to be equipotent to the continuum; this is possible as infinite terrns are allowed. A class is said to have rank $r$ if it can be defined by a term with $r$ distinct variables. For any given natural number $r$, the number of term-definable classes of rank $r$ is shown to be finite, and the classes of rank 0 or 1 are completely described. Many concrete examples of term-definable classes of Boolean functions are also considered.
\itemrv{Magnus Steinby (Turku)}
\itemcc{B.6.3}
\itemut{Boolean functions; functional terms; term-definable classes; closure properties; clone}
\itemli{}
\end