A biomolecular, programmable 3-symbol-3-state finite automaton is reported. This automaton computes autonomously with all of its components, including hardware, software, input, and output being biomolecules mixed together in solution. The hardware consisted of two enzymes: an endonuclease, BbvI, and T4 DNA ligase. The software (transition rules represented by transition molecules) and the input were double-stranded (ds) DNA oligomers. Computation was carried out by autonomous processing of the input molecules via repetitive cycles of restriction, hybridization, and ligation reactions to produce a final-state output in the form of a dsDNA molecule. The 3-symbol-3-state deterministic automaton is an extension of the 2-symbol-2-state automaton previously reported, and theoretically it can be further expanded to a 37-symbol-3-state automaton. The applicability of this design was further amplified by employing surface-anchored input molecules, using the surface plasmon resonance technology to monitor the computation steps in real time. Computation was performed by alternating the feed solutions between endonuclease and a solution containing the ligase, ATP, and appropriate transition molecules. The output detection involved final ligation with one of three soluble detection molecules. Parallel computation and stepwise detection were carried out automatically with a Biacore chip that was loaded with four different inputs.