Abstract:
We consider a functional system of non-homogeneous
functions
\[
f\colon \{0,1\}^{n}\to C,\qquad C\in \{\{0,1\},\{0,3\}\}
\]
with delays
$t\in {\N}_{0}=\{0,1,2,\ldots \}$, i.e., the set of pairs $(f,t)$
with operations of synchronous superposition. For this system we
give the description of all
$\phi$-complete sets in terms of precomplete classes. A set is $\phi$-complete
if using its elements and the operations mentioned above the pair
$(f,t)$ for any function $f$ can be obtained. This description implies the
algorithmic solvability of the $\phi$-completeness problem.