Great advances in biotechnology have allowed the construction of a computer from DNA. One of the proposed solutions is a biomolecular finite automaton, a simple two-state DNA computer without memory, which was presented by Ehud Shapiro’s group at the Weizmann Institute of Science. The main problem with this computer, in which biomolecules carry out logical operations, is its complexity – increasing the number of states of biomolecular automata. In this study, we constructed (in laboratory conditions) a six-state DNA computer that uses two endonucleases (e.g. Acu I and Bbv I) and a ligase. We have presented a detailed experimental verification of its feasibility. We described the effect of the number of states, the length of input data, and the nondeterminism on the computing process. We also tested different automata (with three, four, and six states) running on various accepted input words of different lengths such as ab , aab , aaab , ababa , and of an unaccepted word ba . Moreover, this article presents the reaction optimization and the methods of eliminating certain biochemical problems occurring in the implementation of a biomolecular DNA automaton based on two endonucleases.