An order-optimal method for the synthesis of a search operator in a class of automaton circuits of a special form

We consider a problem of constructing operators of metric closeness in the $n$-dimensional cube in the class of automaton circuits of a special form. We study two characteristics of complexity, the spacial and temporal characteristics (the number of elements of the circuit and the time required for calculations realised by the circuit). We suggest a method of constructing the circuits realising such operators with constant running time and optimal in order number of elements.
This research was supported by the Russian Foundation for Basic Research, grant 01–01–00748.