On solutions to systems of automata-type functional equations

The automata-type functional equations are considered. These equations include subject variables for natural numbers and one-placed functional variables for infinite binary sequences. An algorithm is defined which solves the satisfiability problem for finite systems of functional equations containing only functions $1$ and $t+1$. The linear homogeneous structures are used to establish the lower bound for time complexity of similar deciding algorithms. It is proved that the satisfiability problem is algorithmically undecidable for the systems of functional equations which contain yet the functions $2t,3t$, and $5t$. Tab. 1, bibliogr. 10.