Abstract:
Functions of the algebra of logic that can be realized by
repetition-free formulas over finite bases are studied. Necessary
and sufficient conditions are derived under which functions of the
algebra of logic are repetition-free in pre-elementary bases
$\{-,\cdot,\vee,0,1,x_1\cdot\ldots\cdot x_n\vee
\bar{x}_1\cdot\ldots\cdot \bar{x}_n\}$ and
$\{-,\cdot,\vee,0,1,x_1(x_2\vee
x_3\cdot\ldots\cdot x_n)\vee
x_2\bar{x}_3 \cdot\ldots\cdot\bar{x}_n\}$ where $n\geq 4$. This
completes the description of classes of repetition-free functions of
the algebra of logic in all pre-elementary bases.
Keywords:functions of algebra of logic, repetition-free function,
pre-elementary basis, formula.
Fulltext:
PDF file (206 kB)
