Erratum to "The computational power of Benenson automata" [Theoret. Comput. Sci. 344 (2005) 279-297]

We erroneously claim that Lemma 5.1 applies to both non-deterministic and deterministic Benenson automata, while it applies only to deterministic ones. The following corrected lemma holds for both deterministic and non-deterministic Benenson automata. It also exponentially improves on the dependence on D for both for circuit depth and size compared to the paper version. Note that compared with the paper version, the circuit depth has an extra logarithmic dependence on n, and the circuit size has an extra linear dependence on n. Theorem 3.2 follows from Lemma 5.1(corrected) as before, by taking D = O(1), S = O(log n), and L = poly(n). Lemma 5.1 (Corrected). A function f : {0, 1}n → {0, 1} computed, possibly non-deterministically, by a Benenson automaton (S,D, L, Σ, n, σ , R) can be computed by a O(log(L/D) logD + log2 D + log n) depth, O(LD2 logD + LDn) size circuit.