In this paper we give a new proof of Richardson's theorem [31]: a global function G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] of a cellular automaton [MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is injective if and only if the inverse of G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular automata formulated by Durand (...) [12]. (shrink)